Solve ydx-xdy=xydy

$$y d x - x d y = x y d y$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

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

$$ydx-xdy=xy^{2}d$$

Combine ydx and -xdy to get 0.

$$0=xy^{2}d$$

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

$$xy^{2}d=0$$

Divide 0 by xy^{2}.

$$d=0$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$ydx-xdy=xy^{2}d$$

Combine ydx and -xdy to get 0.

$$0=xy^{2}d$$

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

$$xy^{2}d=0$$

The equation is in standard form.

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

Divide 0 by y^{2}d.

$$x=0$$

Solve for d

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

Steps for Solving Linear Equation

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

$$ydx-xdy=xy^{2}d$$

Combine ydx and -xdy to get 0.

$$0=xy^{2}d$$

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

$$xy^{2}d=0$$

Divide 0 by xy^{2}.

$$d=0$$

Solve for x

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

Steps for Solving Linear Equation

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

$$ydx-xdy=xy^{2}d$$

Combine ydx and -xdy to get 0.

$$0=xy^{2}d$$

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

$$xy^{2}d=0$$

The equation is in standard form.

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

Divide 0 by y^{2}d.

$$x=0$$