Solve x^4=x/2y

$${ x }^{ 4 } = \frac{ x }{ 2y }$$

Solve for y

$$\left\{\begin{matrix}y=\frac{1}{2x^{3}}\text{, }&x\neq 0\\y\neq 0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2y.

$$2yx^{4}=x$$

The equation is in standard form.

$$2x^{4}y=x$$

Divide both sides by 2x^{4}.

$$\frac{2x^{4}y}{2x^{4}}=\frac{x}{2x^{4}}$$

Dividing by 2x^{4} undoes the multiplication by 2x^{4}.

$$y=\frac{x}{2x^{4}}$$

Divide x by 2x^{4}.

$$y=\frac{1}{2x^{3}}$$

Variable y cannot be equal to 0.

$$y=\frac{1}{2x^{3}}\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=\frac{2^{\frac{2}{3}}y^{-\frac{1}{3}}}{2}$$

$$x=0$$

$$x=\frac{2^{\frac{2}{3}}e^{\frac{2\pi i}{3}}y^{-\frac{1}{3}}}{2}$$

$$x=\frac{2^{\frac{2}{3}}e^{\frac{4\pi i}{3}}y^{-\frac{1}{3}}}{2}\text{, }y\neq 0$$

Solve for x

$$x=\frac{2^{\frac{2}{3}}}{2\sqrt[3]{y}}$$

$$x=0\text{, }y\neq 0$$