Solve the following differential equation: (1 + x²)(dy)/(dx) + 2xy = 4x² (Application)

Divide by $1+x^2$: $\frac{dy}{dx} + \frac{2x}{1+x^2}y = \frac{4x^2}{1+x^2}$. I.F. $= e^{\int \frac{2x}{1+x^2}dx} = 1+x^2$. Then $y(1+x^2) = \int 4x^2\,dx = \frac{4x^3}{3} + c$. Solution: $y(1+x^2) = \frac{4x^3}{3} + c$