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Homework Help: Satisfy the Differential Equation - Linear Equation

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the function satisfying the differential equation:

    dy/dx - 3y = 6e^(5x)

    with y(0) = -6

    2. Relevant equations

    I believe this is Linear, so it is dy/dx + P(x)y = f(x)

    3. The attempt at a solution

    I chose -3y to be P and used it to obtain integrating factor e^(-3x). I multiplied it though and ended up with d/dx(e^(-3x)y) = 6e^(2x)

    I integrated both sides and got e^(-3x)y = 3e^2x + C

    Solving for C gets me -9 so the satisfying function is y=e^(3x)(3e^(2x)-9)

    When I try to input this function into Webwork (online homework), it tells me it is incorrect and that the variable 'x' is not defined in this context.

    I wanted to make sure I am correct or if somehow, x comes out of this equation.
    Last edited: Jan 30, 2012
  2. jcsd
  3. Jan 30, 2012 #2
    I've confirmed that this is correct. The online program wanted a t variable, not x.
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