Eq form: $y^2\cdot y'+y^3=t$ Try use this substitution: $y=u\cdot v, u=u(t), v=v(t) \rightarrow y'=u'\cdot v + v'\cdot u$ and group: $v^3(u^2\cdot u'+u^3)+v'\cdot u^3\cdot v^2=t$ $u^2\cdot u'+u^3=0$, and etc.