I tried to solve numerically this equation by using NDSolve
-y''[x]*x^2 - y'[x]*x + x^2*y[x]^3 + (-x^2 + 1)*y[x] == 0
I know that at x=0 the function must to vanish, instead at infinity it has to tend to 1 (but at x=5 it must to be already near 1)
However, with the condition y=0 Mathematica says
Infinite expression 1/0^2 encountered.
Why? What does it means? I tried whit other boundary conditions but the function always explodes near the origin. Why this problem?
This in not a pure homework as it could seems