Non linear ODE Problems I encountered with this problem very recently  here it is

$\frac{dx}{dt}=-x$

$\frac{dy}{dt}=2x^2 y^2$

Find the critical points

find the different equation of paths

solve equation ti find the paths

I really dont know how to solve this equations, if it is linear format i can work out easily .
The first equation is linear, yielding $x(t)=x_0e^{-t}$.
You can put this into the second equation, giving
$$\frac{dy}{dt}=2x_0^2e^{-2t}y^2$$
which is separable.  Can you take it from there?
afther solved we have:
$$y(t)=\frac1{x_0^2 e^{-2t} +y_0 }$$