(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Obtain the Green's function for BVP (and use it to express the solution for the given data):

-y''(x) = f(x), 0 < x < 1, y'(0) = a, y(1) = b

2. Relevant equations

3. The attempt at a solution

I have found 2 solutions to the homogeneous equation

y1(x) = ax, satisfies y'(0) = a

y2(x) = x - 1 + b, satisfies y(1) = b

Then I need to consider a general solution y(x) = c1(x)y1(x) + c2(x)y2(x)

So y' = c1y1' + c2y2' (imposing c1'y1 + c2'y2 = 0)

y'' = c1y1'' + c2y2'' + c1'y1' + c2'y2'

So to satisfy the boundary conditions I need

a = ac1(0) + c2(0)

b = ac1(1) + bc2(a)

I am not sure how to impose these into the integrals for c1 and c2 (as I would in the case when I have something like y(a) = 0 = y(b)?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Green's function for BVP

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**