[tex]u''+u = f(x)[/tex]

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- November 25th 2010, 10:17 AMCreebeFinding Green's Function for ODE
[tex]u''+u = f(x)[/tex]

- November 26th 2010, 11:55 PMmukmar
1. Solve homogeneous equation

2. for

We note to ensure linear independence of solutions as the Wronskian is .

Hence

3. continuous at

Therefore**Eq. 1**,

4. Jump Condition

Which gives:

**Eq. 2**

Now Eq. 1 and Eq. 2 together give:

Now using Eq. 1 again, we know

Also we can simplify:

So putting this all together, we get our Green's function:

From here you should be able to represent the solution as a sum of two integrals that utilize the Green's function. Good luck :)

P.S. Let me know if I made any mistakes! - November 27th 2010, 08:28 AMCreebe
your answer is correct according to the solution

many thanks!