Solve for A
A=\frac{y^{3}}{e^{2x}}
Solve for x
\left\{\begin{matrix}x=\frac{\ln(\frac{y^{3}}{A})}{2}\text{, }&\left(y<0\text{ and }A<0\right)\text{ or }\left(y>0\text{ and }A>0\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }A=0\end{matrix}\right.
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Ae^{2x}=y^{3}
Swap sides so that all variable terms are on the left hand side.
e^{2x}A=y^{3}
The equation is in standard form.
\frac{e^{2x}A}{e^{2x}}=\frac{y^{3}}{e^{2x}}
Divide both sides by e^{2x}.
A=\frac{y^{3}}{e^{2x}}
Dividing by e^{2x} undoes the multiplication by e^{2x}.
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