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Thread: 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
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    Are you familiar with the method of integrating factor?

    $\displaystyle
    xy' - 2y = x^3 e^x $

    divide the ODE by x:

    $\displaystyle y' - \frac{2}
    {x}y = x^2 e^x $

    thus the integrating factor is:

    $\displaystyle
    \mu = e^{ - \int {\frac{2}
    {x}dx} } = e^{ - 2\ln x} = \frac{1}
    {{x^2 }}$

    read this and try to continue:

    Integrating factor - Wikipedia, the free encyclopedia
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