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Math Help - Separation of variables...

  1. #1
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    Separation of variables...

    how do you determine the solution of the this differential eqation:

    xy'-2y=x^3e^x
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  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
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    Are you familiar with the method of integrating factor?

    <br />
xy' - 2y = x^3 e^x

    divide the ODE by x:

    y' - \frac{2}<br />
{x}y = x^2 e^x

    thus the integrating factor is:

    <br />
\mu  = e^{ - \int {\frac{2}<br />
{x}dx} }  = e^{ - 2\ln x}  = \frac{1}<br />
{{x^2 }}

    read this and try to continue:

    Integrating factor - Wikipedia, the free encyclopedia
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