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## Homework Statement

Find the general solution for: x y' - 2y = x +1 (x>0)

## Homework Equations

None

## The Attempt at a Solution

I have literally no idea how to start this. I've tried seperating variables but ended up with:

[tex]\frac{y'-1}{2y+1}[/tex] = [tex]\frac{1}{x}[/tex] but that isn't solvable due to the y'-1 (at least I don't know how if it is). Any help is greatly appreciated!

Edit: Ok, so I've used integrating factors. If you take the integrating factor to be x

^{-2}(i can show how if needed) and then use that, I find:

[tex]\frac{d}{dx}(x^{-2}y) = x^{-2}+ x^{-3}[/tex] so the equation integrates to:

[tex] y = cx^{2}-x-\frac{1}{2}[/tex] does that seem about right? We have disagreement in our group :/

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