Differential equation: how to start w/ x2(y+1)+y2(x-1)y'=0

[Nico55]

I need to solve the following differential equation: x²(y+1)+y²(x-1)y'=0. Normally I'd start the same way as another linear equation of first order by writing my p(x), q(x) and u(x)=e^{integral(p(x))}, but in this one the y+1, y^2 and x-1 really bother me. Can someone help?

 

[HallsofIvy]

I need to solve the following differential equation: x²(y+1)+y²(x-1)y'=0. Normally I'd start the same way as another linear equation of first order by writing my p(x), q(x) and u(x)=e^{integral(p(x))}, but in this one the y+1, y^2 and x-1 really bother me. Can someone help?

You can't "start the same way as another linear equation" because this is not linear! It is, however, "separable":
\(\displaystyle y^2(x+ 1)y'= -x^2(y+ 1)\) so \(\displaystyle \frac{y^2}{y+1}dy= -\frac{x^2}{x+ 1}dx\).