Solve y=x^2y-x^2

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

Solve for y (complex solution)

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

$$x\neq 1\text{ and }x\neq -1$$

Steps for Solving Linear Equation

Subtract x^{2}y from both sides.

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

Reorder the terms.

$$-yx^{2}+y=-x^{2}$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 1-x^{2}.

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

Dividing by 1-x^{2} undoes the multiplication by 1-x^{2}.

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

Solve for y

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

$$|x|\neq 1$$

Steps for Solving Linear Equation

Subtract x^{2}y from both sides.

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

Reorder the terms.

$$-yx^{2}+y=-x^{2}$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 1-x^{2}.

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

Dividing by 1-x^{2} undoes the multiplication by 1-x^{2}.

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

Solve for x (complex solution)

$$x=-i\left(1-y\right)^{-\frac{1}{2}}\sqrt{y}$$

$$x=i\left(1-y\right)^{-\frac{1}{2}}\sqrt{y}\text{, }y\neq 1$$

Solve for x

$$x=\sqrt{-\frac{y}{1-y}}$$

$$x=-\sqrt{-\frac{y}{1-y}}\text{, }y\leq 0\text{ or }y>1$$