Find a green's function G(x,t) for the BVP y'' + y' = f(x), y(0) = 0, y'(1) = 0.
The Attempt at a Solution
I solved the homogeneous equation, looking for 2 linearly independent solutions, and found A (constant) and exp(-x). I am struggling with the boundary conditions though. My solution y1=A satisfies y1'(1) = 0 but I can't find a solution to satisfy y(0) = 0. If I were to find this, my method would be to write y(x) = c1(x)y1(x) + c2(x)y2(x), then find integral expressions for c1 and c2. However, as I can't find another linearly independent solution to the homogeneous equation do I need to use a different method?