Solve dy/dx=dy/x(y-x)

$$\frac { d y } { d x } = \frac { d y } { x ( y - x ) }$$

Solve for d

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(-x+y\right).

$$x\left(-x+y\right)\frac{\mathrm{d}(y)}{\mathrm{d}x}=dy$$

Use the distributive property to multiply x by -x+y.

$$\left(-x^{2}+xy\right)\frac{\mathrm{d}(y)}{\mathrm{d}x}=dy$$

Use the distributive property to multiply -x^{2}+xy by \frac{\mathrm{d}(y)}{\mathrm{d}x}.

$$-x^{2}\frac{\mathrm{d}(y)}{\mathrm{d}x}+xy\frac{\mathrm{d}(y)}{\mathrm{d}x}=dy$$

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

$$dy=-x^{2}\frac{\mathrm{d}(y)}{\mathrm{d}x}+xy\frac{\mathrm{d}(y)}{\mathrm{d}x}$$

The equation is in standard form.

$$yd=0$$

Divide 0 by y.

$$d=0$$

Solve for x

$$x\in \mathrm{R}\setminus 0,y,y=0\text{ or }d=0$$