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Solving equations using Laplace transform

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Aleem Andrew
Aleem Andrew el 14 de En. de 2021
Respondida: Logeshwari S el 19 de Nov. de 2021
I am trying to solve an equation using the Laplace transform without having to find the Laplace transforms of the terms in the equation. Matlab is unable to find a solution based on the code below, although a solution can be found by writing the terms as a function of s. Could someone please suggest a method to do this?
syms y(t)
Dy2 = diff(y,t,2); Dy1 = diff(y,t,1);
eqn = laplace(Dy2+3*Dy1+2*y) == laplace(exp(-t))
cond = [y(0)==4, Dy(0)==5];
sol = dsolve(eqn,cond)
f

Respuesta aceptada

Star Strider
Star Strider el 14 de En. de 2021
Unless you are solving a partial differential equation, such that the Laplace transform produces an ordinary differential equation in one of the two variables and a Laplace transform of ‘t’, dsolve is not appropriate. It is simply necessary to solve for (in this instance) ‘Y(s)’ and then invert it to get ‘y(t)’:
syms t y(t) Y(s) Dy0
Dy2 = diff(y,t,2);
Dy1 = diff(y,t,1);
eqn = laplace(Dy2+3*Dy1+2*y == exp(-t))
eqn = subs(eqn, {laplace(y(t), t, s), subs(diff(y(t), t), t, 0)},{Y(s), Dy0})
cond = [y(0)==4, Dy1(0)==5];
Soln_s = isolate(eqn, Y(s))
Soln_t = ilaplace(Soln_s)
Soln_t = subs(Soln_t, {ilaplace(Y(s), s, t)}, {y(t)})
Soln_t = simplify(Soln_t, 'Steps',500)
.
  6 comentarios
Aleem Andrew
Aleem Andrew el 14 de En. de 2021
Thank you. You have been very helpful
Star Strider
Star Strider el 14 de En. de 2021
As always, my pleasure!

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Logeshwari S
Logeshwari S el 19 de Nov. de 2021
clear all clc syms x w f=input('Enter the function of x: '); F=laplace(f,x,w); disp('Laplace transform of f(t) = '); disp(F);

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