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Math Help - First-order differential equation (Laplace)

  1. #1
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    First-order differential equation (Laplace)

    I am given the instructions "find a general solution to the equation"

    given: y' + 2y = y^2 * e^x

    i was able to take the laplace of the entire equation and what i got was

    Sy(s) - y(0) + 2(y(s)) = 2 / (s-1)^3

    the next part of this problem would be to plug in the givens and usually i would be given what y(0) equals to. how am i suppose to solve this transformation if i am unable to cancel out y(0)? was there something i was suppose to do to find the value of y(0)?

    the answer i was provided is: y(e^x + Ce^2x) = 1; y = 0

    this is on my practice final and any help would be much appreciated!
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  2. #2
    A Plied Mathematician
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    Do you have to use the LT? I'm not sure of its effectiveness on a nonlinear equation like you have. On the other hand, your equation is Bernoulli. That's probably how I would attack it.
    Last edited by Ackbeet; June 8th 2011 at 05:22 AM.
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