# Green's Function fo a Boundary Value Problem

1. Nov 26, 2012

### maxtor101

1. The problem statement, all variables and given/known data

$$L[y] = \frac{d^2y}{dx^2}$$

Show that the Green's function for the boundary value problem with $y(-1) = 0$ and $y(1) = 0$ is given by

$G(x,y) = \frac{1}{2}(1-x)(1+y) for -1\leq y \leq x \leq 1\$

$G(x,y) = \frac{1}{2}(1+x)(1-y) for -1\leq x \leq y \leq 1\$

2. Relevant equations

3. The attempt at a solution

Well in class we had defined $L[y] = (py')' + qy$ as the Strum-Liouville self-adjoint operator

So that gives me:

$L[y] = (py')' + qy = \frac{d^2y}{dx^2}$

Do I treat this problem like other Strum-Liouville Boundary Problems by writting it as :

$L[y] = (py')' + qy = f(x)$

Where $f(x) = \frac{d^2y}{dx^2}$

And continue on as I usually would?

Any help on this would be greatly appreciated!