Y"+2xy'^2=0

(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=1y=1/[ln|x^2-1|+1]