(x^2+1)y'=4x^3-2xy,即 y'+[2x/(x^2+1)]y=4x^3/(x^2+1) 是一阶线性微分方程,则y = e^[-∫2xdx/(x^2+1)]{∫4x^3/(x^2+1) e^[∫2xdx/(x^2+1)]dx+C}= [1/(x^2+1)](∫4x^3dx+C)= (x^4+C)/(x^2+1).