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## Homework Statement

use an integrating factor to solve

[tex]

\frac{ \partial u}{ \partial x} = -2 + \frac{u}{2x}

[/tex]

## The Attempt at a Solution

let P(x) = [tex] \frac {1}{2x} [/tex]

M(x) = [tex] e^(\int(\frac {1}{2x}dx)) [/tex]

= [tex]\sqrt{x}[/tex]

so u = [tex]

\frac{1}{ \sqrt{x}} \int-2\sqrt{x} dx = \frac{1}{ \sqrt{x}}(\frac{2}{3} x^(3/2))

[/tex]

=-4x + k

anyone got any ideas if im doing this right?

thanks