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Solve BVP using Eigenfunction Expansion

  1. May 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve BVP y''[x]-y[x]=Cos[2x] using eigenfunction expansion.
    We know y'[0]=y'[Pi]=0

    2. Relevant equations

    Fourier it up

    3. The attempt at a solution
    Is the corresponding Sturm-Liouville problem:
    f''[x]+/lambda*f=0?

    All the examples we've done have been of form y''[x]+y[x]=g[x] but does a negative sign in front of y[x] change the corresponding S/L problem we use?

    It follows that f[x]=Cosnx

    Because I proceed to solve for y[x]=Sum[A_n*f[x]] and I find the coefficents and all but when I plot my Fourier expansion for y[x], it is very different from the actual result of y[x]. I'm guessing I wasn't supposed to use f''[x]+/lambda*f=0 to find my eigenfunction expansion, but I'm confused as to why I'm getting the wrong answer
     
  2. jcsd
  3. May 2, 2012 #2
    Edit: sorry i misunderstood
     
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