Solve the following equation using Green's functions:
$u''-k^2u=f$ with boundary conditions $u(0)-u'(0)=a$ and $u(1)=b$
For this problem, I was going to find the green's function with homogeneous BC's (set both BC's equal to zero), and then I was going to add the solution to the homogeneous equation Lu = 0 (with the BC's given above) to the green's function solution. However, when working out the green's function, I end up with constant that can't be solved. Any help?