Solve +(x^2y-x)dy=0

$$+ ( x ^ { 2 } y - x ) d y = 0$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&y=0\text{ or }x=\frac{1}{y}\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2}y-x by d.

$$\left(x^{2}yd-xd\right)y=0$$

Use the distributive property to multiply x^{2}yd-xd by y.

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

Combine all terms containing d.

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

Divide 0 by x^{2}y^{2}-xy.

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=0\text{ or }x=\frac{1}{y}\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2}y-x by d.

$$\left(x^{2}yd-xd\right)y=0$$

Use the distributive property to multiply x^{2}yd-xd by y.

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

Combine all terms containing d.

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

Divide 0 by x^{2}y^{2}-xy.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{1}{y}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ or }d=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{1}{y}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ or }d=0\end{matrix}\right.$$