Problem 51783. Solve an ODE: equation B

Write a function to solve the following ordinary differential equation:
y" + (1/x) y' - (a^2 + p^2/x^2) y = 0
with y(x1) = y1 and either y(x0) = y0 or y'(x0) = y'0. Along with y1, one of y0 and yp0 will be assigned numerical values, and the other will be NaN. The function should return the values of y at the specified values of x.
One of the applications for this equation is in groundwater. For a = 1 and p = 0 the equation arises in the flow of water to a well pumping in a leaky confined aquifer; the independent variable x is the normalized distance from the well, and y is related to the piezometric head, a combination of the elevation and pressure of the water. Specifying the derivative at a point amounts to specifying the flow to the well.
Solve

Solution Stats

31.82% Correct | 68.18% Incorrect
Last Solution submitted on May 09, 2025

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