Solve y=xy-1/y^2

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

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

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

$$yy^{2}=xyy^{2}-1$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$y^{3}=xyy^{2}-1$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$y^{3}=xy^{3}-1$$

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

$$xy^{3}-1=y^{3}$$

Add 1 to both sides.

$$xy^{3}=y^{3}+1$$

The equation is in standard form.

$$y^{3}x=y^{3}+1$$

Divide both sides by y^{3}.

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

Dividing by y^{3} undoes the multiplication by y^{3}.

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

Divide y^{3}+1 by y^{3}.

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

Solve for y (complex solution)

$$y=-\left(1-x\right)^{-\frac{1}{3}}$$

$$y=e^{\frac{\pi i}{3}}\left(1-x\right)^{-\frac{1}{3}}$$

$$y=e^{\frac{5i\pi }{3}}\left(1-x\right)^{-\frac{1}{3}}\text{, }x\neq 1$$

Solve for y

$$y=-\frac{1}{\sqrt[3]{1-x}}$$

$$x\neq 1$$