Solve y=x^3f(x)

$$y = x ^ { 3 } f ( x )$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{y}{x^{4}}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$y=x^{4}f$$

Swap sides so that all variable terms are on the left hand side.

$$x^{4}f=y$$

Divide both sides by x^{4}.

$$\frac{x^{4}f}{x^{4}}=\frac{y}{x^{4}}$$

Dividing by x^{4} undoes the multiplication by x^{4}.

$$f=\frac{y}{x^{4}}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{y}{x^{4}}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$y=x^{4}f$$

Swap sides so that all variable terms are on the left hand side.

$$x^{4}f=y$$

Divide both sides by x^{4}.

$$\frac{x^{4}f}{x^{4}}=\frac{y}{x^{4}}$$

Dividing by x^{4} undoes the multiplication by x^{4}.

$$f=\frac{y}{x^{4}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=if^{-\frac{1}{4}}\sqrt[4]{y}\text{; }x=f^{-\frac{1}{4}}\sqrt[4]{y}\text{; }x=-f^{-\frac{1}{4}}\sqrt[4]{y}\text{; }x=-if^{-\frac{1}{4}}\sqrt[4]{y}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }f=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt[4]{\frac{y}{f}}\text{; }x=-\sqrt[4]{\frac{y}{f}}\text{, }&\left(y\leq 0\text{ and }f<0\right)\text{ or }\left(y\geq 0\text{ and }f>0\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }f=0\end{matrix}\right.$$