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## Homework Statement

I'm trying to study for a quiz tomorrow by doing some practice problems. If someone could help me with the process of solving a 1st order linear diff. eq., that would be great.

(x+1)(dy/dx) + (x+2)y = 2xe

^{-x}

## Homework Equations

## The Attempt at a Solution

dy/dx + [(x+2)/(x+1)]y = 2xe

^{-x}/(x+1)

integrating factor: e

^{∫(x+2)/(x+1)}= e

^{x}lx+1l

This is where I get confused. I should be able to use the product rule here:

(y(e

^{x}lx+1l)'

so that I will be able to take the integral of (above) and {2xe

^{-x}/(x+1)]*[e

^{x}lx+1l].

Once I take the integrals, then I can solve for c(not in this problem, though) and try to solve for y explicitly. Some help with the middle steps would be greatly appreciated.