Solve psiphi=xy^2

$$\psi \phi = x y ^ { 2 }$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$xy^{2}=\psi ϕ$$

The equation is in standard form.

$$y^{2}x=\psi ϕ$$

Divide both sides by y^{2}.

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

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

$$x=\frac{\psi ϕ}{y^{2}}$$

Solve for x

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

Steps for Solving Linear Equation

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

$$xy^{2}=\psi ϕ$$

The equation is in standard form.

$$y^{2}x=\psi ϕ$$

Divide both sides by y^{2}.

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

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

$$x=\frac{\psi ϕ}{y^{2}}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=-x^{-\frac{1}{2}}\sqrt{\psi }\sqrt{ϕ}\text{; }y=x^{-\frac{1}{2}}\sqrt{\psi }\sqrt{ϕ}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&\left(\psi =0\text{ or }ϕ=0\right)\text{ and }x=0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\sqrt{\frac{\psi ϕ}{x}}\text{; }y=-\sqrt{\frac{\psi ϕ}{x}}\text{, }&\left(ϕ\leq 0\text{ and }\psi \geq 0\text{ and }x<0\right)\text{ or }\left(ϕ\geq 0\text{ and }\psi \geq 0\text{ and }x>0\right)\text{ or }\left(\psi \leq 0\text{ and }ϕ\leq 0\text{ and }x>0\right)\text{ or }\left(\psi \leq 0\text{ and }ϕ\geq 0\text{ and }x<0\right)\\y\in \mathrm{R}\text{, }&\left(\psi =0\text{ or }ϕ=0\right)\text{ and }x=0\end{matrix}\right.$$