$ (\tan y -2xy-y)dx-(x^2-x\tan^2 y+\sec^2 y)dy=0\\ M=\tan y -2xy-y \\ N=-(x^2-x\tan^2 y+\sec^2 y)$

$$ \frac{\partial{M}}{\partial{y}}=sec^2y-2x-1=\tan^2y-2x\\ \frac{\partial{N}}{\partial{x}}=\tan^2y-2x \\ \frac{\partial{M}}{\partial{y}}=\frac{\partial{N}}{\partial{x}}$$

The given Equation is an exact differential equation.

Solution is given by

$\int Mdx+\int(Terms\ in\ N\ not\ containg\ x)dy=c \\ y=constant$

$$\int(\tan y-2xy-y)dx-\int\sec^2ydy=c\\ x\tan y-x^2y-xy-\tan y=c $$