I'm trying to solve this non-linear differential equation : $$ \frac{dy}{dx}= \frac{y^3}{(y+1)^2(y+2)^2} $$ with the boundary condition $y(x_0)=x_0$, $x>0$, and $y(x)$ being a positive function.
The equation may look simple to integrate, however after integration i get what looks like a transcendental equation and i can not isolate $y(x)$, Is there any way to solve it?