Finding topological conjugacy between dynamical systems

Question

I want to find a topological conjugacy between $x'=\lambda x,y'=\mu y$ such that $λμ>0$ . Here's my work: I found the solution for both ODEs, given by $x(t)=Me^{\lambda t},y(t)=Ne^{\mu t}$ for any $M,N\in\mathbb{R}$. Then I chose the difeomorphism $h:\mathbb{R}\to\mathbb{R}$ defined by $h(t)=\lambda t/\mu$. The motivation for this was that $e^{\mu h(t)}=e^{\lambda t}$. Then, is it true that $x=h^{-1}yh$? I seem to find a problem regarding rhe constants. Furthermore, I suspect that solving the ODEs is not required. Thank you in advance.