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