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Homework Help: Find the solution to the initial value problem

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the solution to the initial value problem
    dy/dx - y = e^3x
    y(0) = 3

    2. Relevant equations
    e^∫p(x)

    3. The attempt at a solution
    Do I treat p(x) = -1?
    I(x) = e^∫-1 = e^-x
    e^-x(dy/dx) - ye^-x = e^3x . e^-x
    e^-x(dy/dx) - e^-x . y = e^2x
    e^-x . y = ∫e^2x
    y = (2e^2x + c)/(e^-x)
    y = C+2e^3x?
     
  2. jcsd
  3. Sep 5, 2011 #2

    Hootenanny

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    Staff Emeritus
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    Gold Member

    Yes, in this case p(x)=-1. However, you're answer isn't correct as it doesn't satisfy the initial value problem. You have made a little slit in the second to last line of your working.
     
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