Solve dy=dx/x^2

$$d y = \frac { d x } { x ^ { 2 } }$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}.

$$dyx^{2}=dx$$

Subtract dx from both sides.

$$dyx^{2}-dx=0$$

Combine all terms containing d.

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

Divide 0 by yx^{2}-x.

$$d=0$$

Solve for d

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}.

$$dyx^{2}=dx$$

Subtract dx from both sides.

$$dyx^{2}-dx=0$$

Combine all terms containing d.

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

Divide 0 by yx^{2}-x.

$$d=0$$

Solve for x

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