Solve ydx=(x-1)dy

$$y d x = ( x - 1 ) d y$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by d.

$$ydx=\left(xd-d\right)y$$

Use the distributive property to multiply xd-d by y.

$$ydx=xdy-dy$$

Subtract xdy from both sides.

$$ydx-xdy=-dy$$

Combine ydx and -xdy to get 0.

$$0=-dy$$

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

$$-dy=0$$

The equation is in standard form.

$$\left(-y\right)d=0$$

Divide 0 by -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

Use the distributive property to multiply x-1 by d.

$$ydx=\left(xd-d\right)y$$

Use the distributive property to multiply xd-d by y.

$$ydx=xdy-dy$$

Subtract xdy from both sides.

$$ydx-xdy=-dy$$

Combine ydx and -xdy to get 0.

$$0=-dy$$

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

$$-dy=0$$

The equation is in standard form.

$$\left(-y\right)d=0$$

Divide 0 by -y.

$$d=0$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

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

Solve for x

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

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