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Linear differential equation problem

  1. Dec 3, 2007 #1
    1. The problem statement, all variables and given/known data
    [tex] \ \frac{dy}{dx} + 2y = xe^x [/tex]



    2. Relevant equations



    3. The attempt at a solution
    I'v only ever solved differential equations where values can be seperated easily, i understand i may have to use something called the integrating factor but this does not seem to fit the formula layout of

    [​IMG]
     
  2. jcsd
  3. Dec 3, 2007 #2
    The equation you presented:

    [tex]\frac{dy}{dx}+p(x)\cdot y=q(x)[/tex]

    is a linear differential equation of the first order. This is the next type you learn after the ones you can separate immediately. It has a general solution. What is your knowledge on the ways for solving these? You should have some idea about this, can you show an attempt of solving it?
     
  4. Dec 3, 2007 #3

    Hurkyl

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    Why not? What doesn't match?
     
  5. Dec 3, 2007 #4

    HallsofIvy

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    Remember that p(x) and q(x) can be 'constant functions'.
     
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