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## Homework Statement

Find a green's function G(x,t) for the BVP y'' + y' = f(x), y(0) = 0, y'(1) = 0.

## Homework Equations

## 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 y

_{1}=A satisfies y

_{1}'(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?

Thank you.