Solving Analytically 2nd order Nonlinear ODE

Question

How to solve:

$$\displaystyle \ddot{y} + 3 y \dot{y} + y^3 - t^{-1} (y^2 + \dot{y}) - 2 t^{-2} y - 4 t^{-3} =0$$ ?

where $\dot{y} = \frac{dy}{dt}$

The solution $ y= j t^{-1}$