Solve y=2operatorname{arcctg}pi/2x

$$y = 2 \operatorname { arcctg } \frac { \pi } { 2 } x$$

Solve for x

$$x=\frac{y}{2\arctan(\frac{2}{\pi })}$$

Steps for Solving Linear Equation

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

$$2\arccot(\frac{\pi }{2})x=y$$

Divide both sides by 2\arccot(\frac{1}{2}\pi ).

$$\frac{2\arccot(\frac{\pi }{2})x}{2\arccot(\frac{\pi }{2})}=\frac{y}{2\arccot(\frac{\pi }{2})}$$

Dividing by 2\arccot(\frac{1}{2}\pi ) undoes the multiplication by 2\arccot(\frac{1}{2}\pi ).

$$x=\frac{y}{2\arccot(\frac{\pi }{2})}$$

Divide y by 2\arccot(\frac{1}{2}\pi ).

$$x=\frac{y}{2\arctan(\frac{2}{\pi })}$$

Solve for y

$$y=2\arctan(\frac{2}{\pi })x$$