Solve xydx+dy=0

$$x y d x + d y = 0$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

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

$$x^{2}yd+dy=0$$

Combine all terms containing d.

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

The equation is in standard form.

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

Divide 0 by x^{2}y+y.

$$d=0$$

Solve for d

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

Steps for Solving Linear Equation

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

$$x^{2}yd+dy=0$$

Combine all terms containing d.

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

The equation is in standard form.

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

Divide 0 by x^{2}y+y.

$$d=0$$

Solve for x (complex solution)

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

Solve for x

$$x\in \mathrm{R}$$

$$d=0\text{ or }y=0$$