- #1
maxtor101
- 24
- 0
Homework Statement
[tex] L[y] = \frac{d^2y}{dx^2} [/tex]
Show that the Green's function for the boundary value problem with [itex] y(-1) = 0 [/itex] and [itex] y(1) = 0 [/itex] is given by
[itex] G(x,y) = \frac{1}{2}(1-x)(1+y) for
-1\leq y \leq x \leq 1\ [/itex]
[itex] G(x,y) = \frac{1}{2}(1+x)(1-y) for
-1\leq x \leq y \leq 1\ [/itex]
Homework Equations
The Attempt at a Solution
Well in class we had defined [itex] L[y] = (py')' + qy [/itex] as the Strum-Liouville self-adjoint operator
So that gives me:
[itex] L[y] = (py')' + qy = \frac{d^2y}{dx^2} [/itex]
Do I treat this problem like other Strum-Liouville Boundary Problems by writting it as :
[itex] L[y] = (py')' + qy = f(x) [/itex]
Where [itex] f(x) = \frac{d^2y}{dx^2} [/itex]
And continue on as I usually would?
Any help on this would be greatly appreciated!