I am given the ODE $y'+y=e^{x}y^{\frac{2}{3}}$ and the initial condition $y(0)=0$.
I don't have an idea on how to to this, but the solution in the book starts with letting $u=y^{\frac{1}{3}}$, with this I got to $u'=\frac{1}{3}u + \frac{1}{3}e^x$ and from there I don't know how to continue.
How can I continue and how did the book got to $u=y^{\frac{1}{3}}$ in the first place ?
Edit: I am not looking for the solution $\forall x: y(x)=0$