Solve (u-y)(du+dy)=du-dy

$$( u - y ) ( d u + d y ) = d u - d y$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&u=y\text{ or }u=1-y\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply u-y by du+dy and combine like terms.

$$du^{2}-dy^{2}=du-dy$$

Subtract du from both sides.

$$du^{2}-dy^{2}-du=-dy$$

Add dy to both sides.

$$du^{2}-dy^{2}-du+dy=0$$

Combine all terms containing d.

$$\left(u^{2}-y^{2}-u+y\right)d=0$$

The equation is in standard form.

$$\left(-y^{2}+y+u^{2}-u\right)d=0$$

Divide 0 by u^{2}-y^{2}-u+y.

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&u=y\text{ or }u=1-y\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply u-y by du+dy and combine like terms.

$$du^{2}-dy^{2}=du-dy$$

Subtract du from both sides.

$$du^{2}-dy^{2}-du=-dy$$

Add dy to both sides.

$$du^{2}-dy^{2}-du+dy=0$$

Combine all terms containing d.

$$\left(u^{2}-y^{2}-u+y\right)d=0$$

The equation is in standard form.

$$\left(-y^{2}+y+u^{2}-u\right)d=0$$

Divide 0 by u^{2}-y^{2}-u+y.

$$d=0$$

Solve for u (complex solution)

$$\left\{\begin{matrix}\\u=y\text{; }u=1-y\text{, }&\text{unconditionally}\\u\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Solve for u

$$\left\{\begin{matrix}\\u=y\text{; }u=1-y\text{, }&\text{unconditionally}\\u\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$