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

xy'-2y=x^3e^x

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- Feb 20th 2008, 03:35 PMgot_janeSeparation of variables...
how do you determine the solution of the this differential eqation:

xy'-2y=x^3e^x - Feb 20th 2008, 04:46 PMPeritus
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