Solving the linked set of ODEs:
y" + y = 1-t^2/π^2 for 0 ≤ t ≤ π
y" + y = 0 for t > π
We are given the initial condition that y(0) = y'(0) = 0, and it is also noted that y and y' must be continuous at t = π
The Attempt at a Solution
The non-homogeneous ODE when t is between 0 and π didn't give me too much trouble, but it's the seemingly simpler homogeneous case for t > π that I'm struggling with: everything seems to go to zero!
The root of the characteristic equation is ±i.
That gives a solution of y = A cos t + B sin t, but using the given initial conditions both A and B are 0.
Thanks for any help you can offer.