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Quick Green's function q watch

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    Just a really quick question. I'm given:

    y''+(k^2)y=2kcoskx

    I have to find the solution given the conditions: y(0)=y'(0)=0

    This is an initial value problem, and I get:


    G(x,z)=0 (x<z)
    and G(x,z)=sink(x-z)/k (x>z)

    Right from here I should easily be able to find the solution by carrying out the integral:

    INT(from 0 to x) [2coskz*sink(x-z)dz] but even though the obtained answer satisfies the boundary conditions, I've been told that this is not quite correct. Something like G(x-z) and G(z,z)=0 was mentioned, but I can't see how this will give me the correct answer. In any case, if you can tell me why my approach is incorrect, that would be very helpful.

    Thanks alot.
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    You want y(x) = integral of f(z) G(x,z) dz, but you've got integral of f(x) G(x,z) dz.
 
 
 
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Updated: January 21, 2010

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