How can I prove these two fields are locally topologically conjugated?

Question

The problem is to prove that the fields $x'=x$ and $x'=x^3$ are locally topologically conjugated in the origin. I found that the corresponding flux for the first equation is $\phi(x_0,t)=x_0e^t$.The flux for the second one is $\displaystyle\varphi(x_0,t)=\pm \frac{1}{\frac{1}{x_0}-2t}$ if $x_0 \ne 0$, and the null function if $x_0 = 0$. I tried to find a local diffeomorphism $h$ such that $\phi(h(x_0),t)=h(\varphi(x_0,t))$, but I don't know how to do it.