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## Homework Statement

xy' - (x+1)y = 0, y(0) = 5

## Homework Equations

Well all of the differential equation stuff seems relevant to me. But from the beginning dy/dx + P(x)y = Q(x) and ye

^{integral(P(x)dx)}= integral(Q(x)e

^{integral(P(x)dx)}dx + C. The separation of variables M(x)dx + N(y)dy = 0.

## The Attempt at a Solution

Well I tried following separating everything out: xy' - (x+1)y = 0 y' - ((x+1)/x)y = 0/x then p(x) = -(x+1)/x and e

^{integral(P(x)dx)}= e

^{-integral((x+1)/x dx)}and using some more math we end up with e

^{-x}/x and that is where I fall apart. Do I integrate this new function and then what? I come up with x/e

^{-x}for y and (x-1)e

^{x}for y' but when I put it back into the original equation i get x

^{2}+ x = x

^{2}-x. Where did I go wrong?