Solve y=y/x^2

$$y = \frac { y } { x ^ { 2 } }$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=0\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&x=1\text{ or }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{y}{x^{2}} from both sides.

$$y-\frac{y}{x^{2}}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{x^{2}}{x^{2}}.

$$\frac{yx^{2}}{x^{2}}-\frac{y}{x^{2}}=0$$

Since \frac{yx^{2}}{x^{2}} and \frac{y}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{yx^{2}-y}{x^{2}}=0$$

Multiply both sides of the equation by x^{2}.

$$yx^{2}-y=0$$

Combine all terms containing y.

$$\left(x^{2}-1\right)y=0$$

Divide 0 by x^{2}-1.

$$y=0$$

Solve for y

$$\left\{\begin{matrix}y=0\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&|x|=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{y}{x^{2}} from both sides.

$$y-\frac{y}{x^{2}}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{x^{2}}{x^{2}}.

$$\frac{yx^{2}}{x^{2}}-\frac{y}{x^{2}}=0$$

Since \frac{yx^{2}}{x^{2}} and \frac{y}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{yx^{2}-y}{x^{2}}=0$$

Multiply both sides of the equation by x^{2}.

$$yx^{2}-y=0$$

Combine all terms containing y.

$$\left(x^{2}-1\right)y=0$$

Divide 0 by x^{2}-1.

$$y=0$$

Solve for x

$$\left\{\begin{matrix}\\x=1\text{; }x=-1\text{, }&\text{unconditionally}\\x\neq 0\text{, }&y=0\end{matrix}\right.$$