## 2nd Green Function Question

Consider the BVP

$\displaystyle \frac{d}{dx} \big(p(x) \frac{dy}{dx} \big) + q(x)y = f(x)$

with boundary conditions

$\displaystyle y'(0) = \alpha$ and $\displaystyle y(L) = y_L$

(a) State the equation and boundary conditions satisfied by a suitable Green's function for this problem

(b) In terms of the Green's function from part (a) show that

$\displaystyle y(x) = \int_0^L G(x;x_0)f(x_0) dx_0 + u_L \frac{dG}{dx_0}|_{x_0 = L} + \alpha G(x;x_0)|_{x_0 = 0}$

I really don't understand this