xy' - (x+1)y = 0, y(0) = 5
Well all of the differential equation stuff seems relevant to me. But from the beginning dy/dx + P(x)y = Q(x) and yeintegral(P(x)dx) = integral(Q(x)eintegral(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 eintegral(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)ex for y' but when I put it back into the original equation i get x2 + x = x2 -x. Where did I go wrong?