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Homework Help: First order ODE solution

  1. Aug 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Solve first order ODE


    2. Relevant equations

    [tex]\frac{dy}{dx}=x^2+1+\frac{2}{x}y[/tex]
    Rearranged
    [tex]\frac{dy}{dx}-\frac{2}{x}y=x^2+1[/tex]

    3. The attempt at a solution
    Integrating factor
    [tex]p=\exp(-\int \frac{2}{x})=\exp(-2\ln x)=x^{-2}[/tex]

    Multiplying through by the integrating factor
    [tex]\frac{d}{dy}(x^{-2}y)=x^{-2}[/tex]

    Integrating both sides
    [tex]x^{-2}y=-x^{-1}+C[/tex]

    Dividing through by [tex]x^{-2}[/tex]
    [tex]y=Cx^2-x[/tex]

    The problem comes when I use say, Maple to check the answer, it gives

    [tex]y=x^3+Cx^2-x[/tex]

    Any ideas? Thanks
     
  2. jcsd
  3. Aug 19, 2010 #2

    HallsofIvy

    User Avatar
    Science Advisor

    No, the right hand side of your original equation was [itex]x^2+ 1[/itex]. Multiplying that by [itex]x^{-2}[/itex] gives [itex]1+ x^{-2}[/itex]. You've dropped the "1".

     
  4. Aug 19, 2010 #3
    Thanks
     
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