Solve y=arctan(1-x^2)1/xdy

$$y = \arctan ( 1 - x ^ { 2 } ) \frac { 1 } { x } d y$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{x}{\arctan(1-x^{2})}\text{, }&x\neq 1\text{ and }x\neq -1\text{ and }x\neq 0\\d\in \mathrm{C}\text{, }&y=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$yx=\arctan(1-x^{2})\times 1dy$$

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

$$\arctan(1-x^{2})\times 1dy=yx$$

Reorder the terms.

$$dy\arctan(-x^{2}+1)=xy$$

The equation is in standard form.

$$y\arctan(1-x^{2})d=xy$$

Divide both sides by y\arctan(-x^{2}+1).

$$\frac{y\arctan(1-x^{2})d}{y\arctan(1-x^{2})}=\frac{xy}{y\arctan(1-x^{2})}$$

Dividing by y\arctan(-x^{2}+1) undoes the multiplication by y\arctan(-x^{2}+1).

$$d=\frac{xy}{y\arctan(1-x^{2})}$$

Divide xy by y\arctan(-x^{2}+1).

$$d=\frac{x}{\arctan(1-x^{2})}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{x}{\arctan(1-x^{2})}\text{, }&|x|\neq 1\text{ and }x\neq 0\\d\in \mathrm{R}\text{, }&y=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$yx=\arctan(1-x^{2})\times 1dy$$

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

$$\arctan(1-x^{2})\times 1dy=yx$$

Reorder the terms.

$$dy\arctan(-x^{2}+1)=xy$$

The equation is in standard form.

$$y\arctan(1-x^{2})d=xy$$

Divide both sides by y\arctan(-x^{2}+1).

$$\frac{y\arctan(1-x^{2})d}{y\arctan(1-x^{2})}=\frac{xy}{y\arctan(1-x^{2})}$$

Dividing by y\arctan(-x^{2}+1) undoes the multiplication by y\arctan(-x^{2}+1).

$$d=\frac{xy}{y\arctan(1-x^{2})}$$

Divide xy by y\arctan(-x^{2}+1).

$$d=\frac{x}{\arctan(1-x^{2})}$$