Solve the differential equation (1 + x²)(dy)/(dx) = 4x² - 2xy.

Write as a linear equation: $\frac{dy}{dx} + \frac{2x}{1 + x^2}\,y = \frac{4x^2}{1 + x^2}$. Integrating factor $= e^{\int\frac{2x}{1 + x^2}dx} = e^{\ln(1 + x^2)} = 1 + x^2$. $y(1 + x^2) = \int 4x^2\,dx = \frac{4x^3}{3} + C$ Hence $y = \frac{4x^3 + 3C}{3(1 + x^2)}$, i.e. $y(1 + x^2) = \frac{4x^3}{3} + C$.