# Second order homogeneous ODE with vanishing solution

1. Dec 7, 2011

### CassieG

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.

2. Dec 7, 2011

### vela

Staff Emeritus
The initial conditions don't matter because they're for t=0 and you're looking at the solution for t>pi.

You want to match the solutions in the two regions at t=pi.

3. Dec 7, 2011

### CassieG

Ah, thanks, that helps a lot.