# Separation of variables...

• Feb 20th 2008, 03:35 PM
got_jane
Separation of variables...
how do you determine the solution of the this differential eqation:

xy'-2y=x^3e^x
• Feb 20th 2008, 04:46 PM
Peritus
Are you familiar with the method of integrating factor?

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

divide the ODE by x:

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

thus the integrating factor is:

$
\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