How about the differential equation $x=tx'^2+x'^3$. Can somebody solve it?

my solution:suppose $\dot x$=p,then $x=tp^2+p^3$. 
Then, p=$p^2$+2tp$\dot p$+3$p^2\dot p$, then we can use these function to solve p, but I just find the final result is so complex. I don't know how to continue? Or, does somebody have other kinds of methods? Thank you