Y"+2xy'^2=0

(x^2-1)*y'+2xy^2=0, y(0)=1

(x^2-1)*y'=-2xy^2
y'/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|+C1
1/y=ln|x^2-1|+C3
y=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]