(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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.

3. 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?

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# Need help solving a differential equation

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