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

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers8

Suggested Problems

More from this Author316

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!