{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":51815,"title":"Solve an ODE: equation C","description":"Write a function to solve the following ordinary differential equation: \r\n\r\nwith  and . The parameter  is a constant. The function should return the values of  at the specified values of .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 118.583px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 59.2917px; transform-origin: 407px 59.2917px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209.417px 7.91667px; transform-origin: 209.417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to solve the following ordinary differential equation: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.6667px; text-align: left; transform-origin: 384px 18.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg 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alt=\"(1-x^2) y\u0026quot; - x y' + a^2 y = 0\" style=\"width: 179.5px; height: 37.5px;\" width=\"179.5\" height=\"37.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.3917px 7.91667px; transform-origin: 14.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x0) = y0\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIEAAAAoCAYAAADZs5l2AAADf0lEQVR4nO2b25GqQBRFVw5kYAImQARGYAZkYAamQAyEQA6mYAyk4P1odtFyG6TbBqTmrCprpmSkH2z2eeCAYRiGYRiGYezAHThvON4NKDccz/hADVw3HrMAmh3GNQLUuLtyDwrgAVx2Gt8AKtxF2JMT0PU/jY05AS9+Iy7fgHbvSfxFan5n4wucIC0/2BC5wC/F4pr9Q9Of4o4TwS9xwc1pyzL10BS4WH7BxdNQUqVjoU19EhcKyv5cIbu+zswhBoWEvSqVFEqGvQnlVuf+WHbH1aAtbtNeuDt7jI49cRssFAqWbLbyhqd3PolK5Z3eryPXESJWnD63DK+lOcmp//uaYf2hUOZfo9UcToN0vF9ocAsKHSv796uIcfQZXzwtTnzX/vccam9x803hleHVJIx78z4/doMzbj2rVmGKo1OZdaj00qRjJ6XFNP05UjbsEw3puUoOJ0gRssLYlBuWhG/SrOjihCZQ8/8dnyoCXaAOZ9troLkdLTnU3oT25co6N8wbikvj2F/0740TtlQRVMy7zpiC+LIvdW57o9AbEvBcqLyRySX8CfibdyOcMKZu9NkbZ842C4Z29FTCNMVRRaBke5xwl4TXL3fQZ74WgT8BWf+UC0D6Rvtim6sEin5cJZMxIpCrpbBldRBCFZRv/VMuILfIJoLQBO6EXQCGZDImCTr3Y2icJTlBighU7aSwV3UgxmH5wue1ZxWBJvBgKEumTixbX9qUUT+g4j0v+NQcShHBg337BN+Uub5TnnBi+OS2WUXgT+DBZ1vrWK76msH+/bxAY1SEXSdFBFONryPgh+UHy5pnWUXgX5wld1LNtKWr+XMnnN2rJG1xApg6T6wIUsLUr6G9WZrxZxWBTtixrMaee1jjtzrHZSe8t0pDx0WsCO6s13/YCu3d0gRzFRHEtIKfhC1LffGK8ORUAk4dF7Ei6DjWw6MQLXHJZVYRVJGDg3ODNduZMSK4Mu8qR0AVVMwasomgTBhcNOR5+hdiqQgKnBiPnAuoLxPbe8kiAqkvtde+5rd9l4qg4bgVAQx7mNJoShKBvhHUMljoty3WE0N/ISdKPudEULGeE62F1vXEXQP1UGLxnz5GicDvN3/jAKEJtZnOVzBsjt9PH5/7yjEdwG+YdaQ5wIX3a9kQcTMrM1/rW7lbJmZH/j+DK5+rI8MwDMMwDMMwDMPIyT8ZjIEuGJbJhgAAAABJRU5ErkJggg==\" alt=\"y(x1) = y1\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.725px 7.91667px; transform-origin: 51.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The parameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.967px 7.91667px; transform-origin: 169.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a constant. The function should return the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.95px 7.91667px; transform-origin: 50.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the specified values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = solveODEC(x,a,Xbc,bc)\r\n%  y   = values of the function\r\n%  x   = independent variable\r\n%  a   = parameter in the equation\r\n%  Xbc = [x0 x1], values of x where the boundary conditions are specified\r\n%  bc  = [y0 y1], values of the function at x0 and x1, respectively\r\n\r\n   y = f(x,a,Xbc,bc);\r\nend","test_suite":"%% \r\nx   = [-1/3 -1/4 0 1/4 1/3];\r\na   = 1;\r\nXbc = [-1/2 1/2];\r\nbc  = [2 4];\r\ny   = solveODEC(x,a,Xbc,bc);\r\ny_correct = [2.599319657044238 2.854101966249684 3.464101615137754 3.854101966249684 3.932652990377571];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%% \r\nx   = [-0.6 -0.2 -0.05 0.12 0.2];\r\na   = sqrt(3);\r\nXbc = [-0.7 0.3];\r\nbc  = [0 1];\r\ny   = solveODEC(x,a,Xbc,bc);\r\ny_correct = [0.237055225759061 0.877546669526703 0.995431932094838 1.046546024897035 1.039090864471318];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%% \r\nx   = [-0.8 -0.6 -0.3 -0.15 0.1 0.25 0.375];\r\na   = 2;\r\nXbc = [-0.8 0.4];\r\nbc  = [-1 3];\r\ny   = solveODEC(x,a,Xbc,bc);\r\ny_correct = [-1 1.68647951290722 4.138417234449975 4.687455882945745 4.630189304757032 4.024530246664777 3.199461161409147];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%% \r\nx   = [-0.7 -0.45 -0.2 0.05 0.3 0.55 0.8];\r\na   = pi;\r\nXbc = [-0.9 0.9];\r\nbc  = [-1 1];\r\ny   = solveODEC(x,a,Xbc,bc);\r\ny_correct = [1.764854605944604 2.706629373469937 1.6090059417224112 -0.4259046519843118 -2.225041323571773 -2.630850806938173 -0.6162122684969365];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\na   = 5;\r\nXbc = [-1/2 1/2]; \r\nbc  = [-1 1];\r\ny   = 1;\r\nx   = fzero(@(z) solveODEC(z,a,Xbc,bc)-y,0);\r\nx_correct = 0.104528463267653;\r\nassert(abs(x-x_correct)\u003c1e-13)\r\n\r\n%%\r\na   = 5;\r\nXbc = [-1/2 1/2]; \r\nbc  = [-1 1];\r\ny   = 1;\r\nx   = fzero(@(z) solveODEC(z,a,Xbc,bc)-y,0);\r\nx_correct = 0.104528463267653;\r\nassert(abs(x-x_correct)\u003c1e-13)\r\n\r\n%%\r\na   = 2*randi(4)+1;\r\nXbc = [-3/4 3/4]; \r\nbc  = [-2 2];\r\nx   = rand-3/4;\r\nym  = solveODEC(-x,a,Xbc,bc);\r\nyp  = solveODEC(x,a,Xbc,bc);\r\nassert(abs(ym+yp)\u003c1e-13)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-25T04:18:45.000Z","updated_at":"2021-05-25T04:23:56.000Z","published_at":"2021-05-25T04:23:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to solve the following ordinary differential equation: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(1-x^2) y\u0026quot; - x y' + a^2 y = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(1-x^2)\\\\frac{d^2y}{dx^2} -x \\\\frac{dy}{dx}+a^2 y = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x0) = y0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_0) = y_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x1) = y1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_1) = y_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The parameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a constant. The function should return the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the specified values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":51815,"title":"Solve an ODE: equation C","description":"Write a function to solve the following ordinary differential equation: \r\n\r\nwith  and . The parameter  is a constant. The function should return the values of  at the specified values of .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 118.583px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 59.2917px; transform-origin: 407px 59.2917px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209.417px 7.91667px; transform-origin: 209.417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to solve the following ordinary differential equation: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.6667px; text-align: left; transform-origin: 384px 18.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"(1-x^2) y\u0026quot; - x y' + a^2 y = 0\" style=\"width: 179.5px; height: 37.5px;\" width=\"179.5\" height=\"37.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.3917px 7.91667px; transform-origin: 14.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x0) = y0\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y(x1) = y1\" style=\"width: 64.5px; height: 20px;\" width=\"64.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.725px 7.91667px; transform-origin: 51.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The parameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.967px 7.91667px; transform-origin: 169.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a constant. The function should return the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.95px 7.91667px; transform-origin: 50.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the specified values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = solveODEC(x,a,Xbc,bc)\r\n%  y   = values of the function\r\n%  x   = independent variable\r\n%  a   = parameter in the equation\r\n%  Xbc = [x0 x1], values of x where the boundary conditions are specified\r\n%  bc  = [y0 y1], values of the function at x0 and x1, respectively\r\n\r\n   y = f(x,a,Xbc,bc);\r\nend","test_suite":"%% \r\nx   = [-1/3 -1/4 0 1/4 1/3];\r\na   = 1;\r\nXbc = [-1/2 1/2];\r\nbc  = [2 4];\r\ny   = solveODEC(x,a,Xbc,bc);\r\ny_correct = [2.599319657044238 2.854101966249684 3.464101615137754 3.854101966249684 3.932652990377571];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%% \r\nx   = [-0.6 -0.2 -0.05 0.12 0.2];\r\na   = sqrt(3);\r\nXbc = [-0.7 0.3];\r\nbc  = [0 1];\r\ny   = solveODEC(x,a,Xbc,bc);\r\ny_correct = [0.237055225759061 0.877546669526703 0.995431932094838 1.046546024897035 1.039090864471318];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%% \r\nx   = [-0.8 -0.6 -0.3 -0.15 0.1 0.25 0.375];\r\na   = 2;\r\nXbc = [-0.8 0.4];\r\nbc  = [-1 3];\r\ny   = solveODEC(x,a,Xbc,bc);\r\ny_correct = [-1 1.68647951290722 4.138417234449975 4.687455882945745 4.630189304757032 4.024530246664777 3.199461161409147];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%% \r\nx   = [-0.7 -0.45 -0.2 0.05 0.3 0.55 0.8];\r\na   = pi;\r\nXbc = [-0.9 0.9];\r\nbc  = [-1 1];\r\ny   = solveODEC(x,a,Xbc,bc);\r\ny_correct = [1.764854605944604 2.706629373469937 1.6090059417224112 -0.4259046519843118 -2.225041323571773 -2.630850806938173 -0.6162122684969365];\r\nassert(all(abs(y-y_correct)\u003c1e-13))\r\n\r\n%%\r\na   = 5;\r\nXbc = [-1/2 1/2]; \r\nbc  = [-1 1];\r\ny   = 1;\r\nx   = fzero(@(z) solveODEC(z,a,Xbc,bc)-y,0);\r\nx_correct = 0.104528463267653;\r\nassert(abs(x-x_correct)\u003c1e-13)\r\n\r\n%%\r\na   = 5;\r\nXbc = [-1/2 1/2]; \r\nbc  = [-1 1];\r\ny   = 1;\r\nx   = fzero(@(z) solveODEC(z,a,Xbc,bc)-y,0);\r\nx_correct = 0.104528463267653;\r\nassert(abs(x-x_correct)\u003c1e-13)\r\n\r\n%%\r\na   = 2*randi(4)+1;\r\nXbc = [-3/4 3/4]; \r\nbc  = [-2 2];\r\nx   = rand-3/4;\r\nym  = solveODEC(-x,a,Xbc,bc);\r\nyp  = solveODEC(x,a,Xbc,bc);\r\nassert(abs(ym+yp)\u003c1e-13)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-25T04:18:45.000Z","updated_at":"2021-05-25T04:23:56.000Z","published_at":"2021-05-25T04:23:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to solve the following ordinary differential equation: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(1-x^2) y\u0026quot; - x y' + a^2 y = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(1-x^2)\\\\frac{d^2y}{dx^2} -x \\\\frac{dy}{dx}+a^2 y = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x0) = y0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_0) = y_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y(x1) = y1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey(x_1) = y_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The parameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a constant. The function should return the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the specified values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"though perhaps not\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"though 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