1. **State the problem:** Solve the differential equation $$\frac{dy}{dx} = \frac{\tan y - 2xy - y}{x^2 - x \tan^2 y + \sec^2 y}.$$\n\n2. **Analyze the equation:** This is a first-order differential equation involving $x$ and $y$. The right side is a rational expression in terms of $x$, $y$, $\tan y$, and $\sec y$.\n\n3. **Rewrite the equation:** Let us denote the numerator as $N = \tan y - 2xy - y$ and the denominator as $D = x^2 - x \tan^2 y + \sec^2 y$. So, $$\frac{dy}{dx} = \frac{N}{D}.$$\n\n4. **Check for separability or substitution:** The equation is complicated; try substitution $u = \tan y$ or $u = y/x$ to simplify.\n\n5. **Try substitution $u = \tan y$:** Then $y = \arctan u$, and $$\frac{dy}{dx} = \frac{1}{1+u^2} \frac{du}{dx}.$$\n\n6. **Rewrite numerator and denominator in terms of $u$:**\n- $\tan y = u$\n- $y = \arctan u$\n- $\tan^2 y = u^2$\n- $\sec^2 y = 1 + u^2$\n\nSo numerator: $N = u - 2x (\arctan u) - \arctan u$\nDenominator: $D = x^2 - x u^2 + 1 + u^2$\n\n7. **Rewrite the differential equation:**\n$$\frac{1}{1+u^2} \frac{du}{dx} = \frac{u - (2x + 1) \arctan u}{x^2 - x u^2 + 1 + u^2}.$$\n\n8. **Multiply both sides by $1+u^2$:**\n$$\frac{du}{dx} = \frac{(1+u^2)(u - (2x + 1) \arctan u)}{x^2 - x u^2 + 1 + u^2}.$$\n\n9. **This is a complicated nonlinear ODE in $u$ and $x$.** No obvious separable or exact form.\n\n10. **Conclusion:** The equation is complex and does not simplify easily with elementary substitutions. It likely requires advanced methods or numerical solutions.\n\n**Final answer:** The differential equation $$\frac{dy}{dx} = \frac{\tan y - 2xy - y}{x^2 - x \tan^2 y + \sec^2 y}$$ can be rewritten using substitution $u=\tan y$ as $$\frac{du}{dx} = \frac{(1+u^2)(u - (2x + 1) \arctan u)}{x^2 - x u^2 + 1 + u^2}$$ but does not simplify to elementary closed form solutions.