Solve -xy-yy+psix=0

$$- x y - y y + \psi x = 0$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Multiply y and y to get y^{2}.

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

Add y^{2} to both sides. Anything plus zero gives itself.

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

Reorder the terms.

$$-xy+x\psi =y^{2}$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -y+\psi .

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

Dividing by -y+\psi undoes the multiplication by -y+\psi .

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

Solve for x

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

Steps for Solving Linear Equation

Multiply y and y to get y^{2}.

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

Add y^{2} to both sides. Anything plus zero gives itself.

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

Reorder the terms.

$$-xy+x\psi =y^{2}$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -y+\psi .

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

Dividing by -y+\psi undoes the multiplication by -y+\psi .

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

Solve for y (complex solution)

$$y=\frac{-\sqrt{x\left(x+4\psi \right)}-x}{2}$$

$$y=\frac{\sqrt{x\left(x+4\psi \right)}-x}{2}$$

Solve for y

$$y=\frac{-\sqrt{x\left(x+4\psi \right)}-x}{2}$$

$$y=\frac{\sqrt{x\left(x+4\psi \right)}-x}{2}\text{, }\left(x\geq 0\text{ or }x\leq -4\psi \right)\text{ and }\left(x\leq 0\text{ or }x\geq -4\psi \right)$$