(x^2-1)*y'+2xy^2=0, y(0)=1
(x^2-1)*y'=-2xy^2y'/y^2=-2x/(x^2-1)∫y'/y^2 dx=-2∫x/(x^2-1) dx∫1/y^2 dy=-∫1/(x^2-1) d(x^2-1)-1/y +C2=-ln|x^2-1|+C11/y=ln|x^2-1|+C3y=1/[ln|x^2-1|+C3]
y(0)=1/[ln|0^2-1|+C3]=1/[ln|-1|+C3]=1/[ln|1|+C3]=1/[0+C3]=1/C3=1 => C3=1
y=1/[ln|x^2-1|+1]