I need some help, I've tried to solve it since yesterday but i failed.As usually, I need to find $y(x)$ which is the solution of the differential equation. Here is the equation:
$$ (1+x^2)y^3dx-(y^2-1)x^3dy = 0,\qquad y(1) = -1 $$
It is supposed to be easy, but I didn't find the right theorem nor formula to use.
Edit: I already developed to get the following equation $$ \frac {1+x^2}{x^3}dx = \frac {y^2-1}{y^3}dy $$
and after integration got:
$$ \frac {-1}{2x^2}+\ln(|x|) = \frac {1}{2y^2}+\ln(|y|) $$
but how can I get $y(x)$ from there ?