Solve (x-y_{0})dx+xdy=0

$$( x - y _ { 0 } ) d x + x d y = 0$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply x-y_{0} by d.

$$\left(xd-y_{0}d\right)x+xdy=0$$

Use the distributive property to multiply xd-y_{0}d by x.

$$dx^{2}-y_{0}dx+xdy=0$$

Combine all terms containing d.

$$\left(x^{2}-y_{0}x+xy\right)d=0$$

The equation is in standard form.

$$\left(x^{2}+xy-xy_{0}\right)d=0$$

Divide 0 by x^{2}-y_{0}x+xy.

$$d=0$$

Solve for d

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

Steps for Solving Linear Equation

Use the distributive property to multiply x-y_{0} by d.

$$\left(xd-y_{0}d\right)x+xdy=0$$

Use the distributive property to multiply xd-y_{0}d by x.

$$dx^{2}-y_{0}dx+xdy=0$$

Combine all terms containing d.

$$\left(x^{2}-y_{0}x+xy\right)d=0$$

The equation is in standard form.

$$\left(x^{2}+xy-xy_{0}\right)d=0$$

Divide 0 by x^{2}-y_{0}x+xy.

$$d=0$$

Solve for x (complex solution)

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

Solve for x

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