Solve xy=x^3

$$x y = x ^ { 3 }$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=x^{2}\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xy=x^{3}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{x^{3}}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{x^{3}}{x}$$

Divide x^{3} by x.

$$y=x^{2}$$

Solve for y

$$\left\{\begin{matrix}\\y=x^{2}\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xy=x^{3}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{x^{3}}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{x^{3}}{x}$$

Divide x^{3} by x.

$$y=x^{2}$$

Solve for x (complex solution)

$$x=\sqrt{y}$$

$$x=0$$

$$x=-\sqrt{y}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt{y}\text{; }x=-\sqrt{y}\text{, }&y\geq 0\end{matrix}\right.$$