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Trying to solve a boundary value problem

  1. Nov 15, 2008 #1
    Trying to solve the following boundary value problems.



    y'' + 4y = cos x; y(0) = 0, y(pi) = 0
    y'' + 4y = sin x; y(0) = 0, y(pi) = 0




    The answer key says that there's no solution to the first part, but there is a solution to the 2nd part. I'm really lost and am not sure how to go about this. I'd greatly appreciate everyone's help on this!!!
     
  2. jcsd
  3. Nov 15, 2008 #2

    rock.freak667

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    Were you ever taught to solve 2nd order differential equations with constant coefficients?
     
  4. Nov 15, 2008 #3
    For the most part. If it were y'' + 4y = 0, I'd know what to do. But for some reason, I'm at a mental block with this. Or is this something completely different from what you're asking?
     
  5. Nov 15, 2008 #4

    rock.freak667

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    The first step is to find the complementary solution by solving y''+4y=0. What will y be equal to for this?

    You then find a particular integral for the right side.
     
  6. Nov 15, 2008 #5
    y = A cos 2x + B sin 2x.....that would be the complementary solution. How would I go about finding a particular integral? I was gonna do an integrating factor but I think that's only for first-order ODE.
     
  7. Nov 15, 2008 #6

    rock.freak667

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    If the Right side is cosax,sinax, sinax+cosax, then your particular integral is Asinax+Bcosax.

    To find A and B, you need to substitute back this into the differential equation and then compare coefficients.
     
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