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Homework Help: Differential Equations

  1. Feb 25, 2010 #1
    ex y dy/dx = e-y + e-2x-y

    Is this equation supposed to be solved through separation? I got an answer but it looks very messy. Can somebody check if I am doing this correctly?

    ex y dy/dx = e-y + e-2x-y

    ex y dy/dx = e-y + e-2x e-y

    ex y dy/dx = e-y ( 1 + e-2x )

    ey y dy = e-x ( 1 + e-2x ) dx

    Then Integrated by parts on both sides and got this solution:

    ey (y-1) = -e-x - 1/3 e-3x

    Normally I would check it by plugging y and y' in to the differential equation but I dont know how to take the derivative of y in this particular solution.
     
  2. jcsd
  3. Feb 26, 2010 #2

    tiny-tim

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    Hi jofree87! :smile:
    Looks fine. :smile:

    (and i'm afraid you can't always check by differentiating! :wink:)
     
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