1. The problem statement, all variables and given/known data solve y(xy+1)dx + x(1+x^2y^2)dy=0 3. The attempt at a solution well, I substituted u=xy. Here is what I've done so far. du = xdy + ydx -> xdy= du - ydx -> xdy = du - (u/x)dx (u/x)(u+1)dx + x(1+u^2)dy=0 (u/x)(u+1)dx + (1 + u^2)(du - (u/x)dx)=0 (u^2/x)dx + (u/x)dx + du - (u/x)dx + (u^2)du - (u^3/x)dx = 0 (u^2)dx + xdu + (u^2x)du - (u^3)dx = 0 dx/x + (1+u^2)/(u^2 - u^3)du = 0 hence, dx/x = (1+u^2)/(u^3 - u^2)du, if we integrate it we'll have: ln|x| = -ln|u| + ln|u+1| + ln|u-1| + C ln|x| = ln|(u^2 - 1)/u| + lnC' x = C(u^2 -1)/u -> x = C(xy - 1/(xy)). but the book says that the final answer is ln|(1-xy)^2/y| + 1/(xy) = C. :| Have I differentiated u correctly? I can't find out why my answer is incorrect.