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Thread: Separation of variables...

  1. February 20th 2008, 03:35 PM #1
    got_jane
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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. February 20th 2008, 04:46 PM #2
    Peritus
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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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