Question

$$x y + \tan x = y ^ { 2 }$$

Solve for y (complex solution)

$y=-\frac{\sqrt{2\left(x^{2}\cos(2x)+4\sin(2x)+x^{2}\right)}-2x\cos(x)}{4\cos(x)}$
$y=\frac{\sqrt{2\left(x^{2}\cos(2x)+4\sin(2x)+x^{2}\right)}+2x\cos(x)}{4\cos(x)}\text{, }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}$

Solve for y

$y=\frac{-\frac{\sqrt{\left(x\cos(x)\right)^{2}+2\sin(2x)}}{\cos(x)}+x}{2}$
$y=\frac{\frac{\sqrt{\left(x\cos(x)\right)^{2}+2\sin(2x)}}{\cos(x)}+x}{2}\text{, }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi \left(2n_{1}+1\right)}{2}\text{ and }\left(x\cos(x)\right)^{2}+2\sin(2x)\geq 0$