1. A differential equation is given by

${e}^{-3x}\frac{dy}{dx}=2{e}^{y}$

It is known that $y=0$ when $x=0$.

Solve the differential equation, giving your answer in the form

$p{e}^{3x}+{e}^{-y}=q$

where $p$ and $q$ are rational numbers to be found.