I just did a problem for a final that required us to use a green's function to solve a diff eq. y'' +y/4 = sin(2x)(adsbygoogle = window.adsbygoogle || []).push({});

I went through and solved it and got a really nasty looking thing, but I checked it in wolfram and it works out. Now, my question is this:

After I got the solution from my greens functions, I went through and tried to add in what would be the homogeneous solution, Asin(x/2) + Bcos(x/2) and apply the boundary conditions again to solve for A and B. Both came out to be zero. Is this always the case? Is my integrand of G*f the general solution and not just the particular solution? Was this just a coincidence? I have a few more problems I need to do, most of which are green's functions, and this would be handy to know. If it is the general solution, does it have to do with the fact that I used the homogeneous solution to obtain my Green's solution? (I'm not sure what you want to call it)

Thanks

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# I A somewhat conceptual question about Green's functions

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