Can anyone help me graph an Ordinary Differential equation?

Question

Given a Cauchy problem $y'(x)= \frac{x^2y^3}{1+y^2}$ with initial conditions $y(x_0) = y_0$? I know that the $y=0$ is one solution of the given problem and function is increasing or decreasing for $y_0>0$ and $y_0<0$ respectively for all $x>0$ and we cannot cross the $y≡0$ because doing so would contradict the uniqueness property of the problem. But I can't understand how to graph when $x<0$. Also, how can I apply monotonicity and asymptotic theorem when$x\rightarrow-∞$? Is it possible to graph without taking a second derivative?