Solve y=2xy^2

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

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$2xy^{2}=y$$

The equation is in standard form.

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

Divide both sides by 2y^{2}.

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

Dividing by 2y^{2} undoes the multiplication by 2y^{2}.

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

Divide y by 2y^{2}.

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

Solve for x

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

Steps for Solving Linear Equation

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

$$2xy^{2}=y$$

The equation is in standard form.

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

Divide both sides by 2y^{2}.

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

Dividing by 2y^{2} undoes the multiplication by 2y^{2}.

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

Divide y by 2y^{2}.

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

Solve for y

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