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Math Help - Boundary Value Problem

  1. #1
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    Exclamation Boundary Value Problem

    Find the values of  \lambda for which the given boundary problem has a unique solution and find the solution

    y''+4y'+(4+9\lambda)y=0
    y(0)=1, y(2)=0

    Please help. I have tried using a new dependent variable u where y=s(x)u but I am not sure if this is right
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  2. #2
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    I would say the first step should be to find the general solution (without the constants of integration determined). You've got a homogeneous equation, so no particular solution is required. What did you get for that?
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  3. #3
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    I got y(x)=Ae^{-2x}cos3x+Be^{-2x}sin3x but i don't think that's even right
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  4. #4
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    I'm afraid it can't possibly be correct: there are no \lambda's in your solution. It's a second-order linear ODE with constant coefficients. I would just use the guess-and-check method (or undetermined coefficients).
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  5. #5
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    Okay, thanks. I will try after I get some sleep (it's 3.30 am here :P ). Thanks again.
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  6. #6
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    Did you manage to get a solution?
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  7. #7
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    Yes I did. Thanks for asking!
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