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Homework Help: Differential Equation isolation

  1. Oct 28, 2007 #1
    Solve the differential equation:

    [tex]\frac{dy}{dx}-\frac{y}{x}=3x^{2}[/tex]

    Where y(1)=3

    Can't figure out how to isolate each side. Played with it forever to no success. Any tips?
     
  2. jcsd
  3. Oct 28, 2007 #2

    rock.freak667

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    Homework Helper

    ...whenever you have a function of the form:

    [tex]\frac{dy}{dx}+Py=Q[/tex] where both P and Q are functions of x..
    you multiply throughout by [itex]e^{\int P dx}[/itex] and then integrate both sides with respect to x...

    HINT: When you multiply throughout by [itex]e^{\int P dx}[/itex] and then integrate both sides with respect to x

    The left hand side becomes [itex]ye^{\int P dx}[/tex]
     
  4. Oct 28, 2007 #3
    If you wanna use separation of variables you can solve the complimentary equation and use variation of parameters.
     
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