1. The problem statement, all variables and given/known data 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 2. Relevant equations See above. 3. 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.