(1+x^2)(dy)/(dx)-(4x^3y)/(1-x^2)=1

解

(1 + x^{2}) \frac{d y}{d x} - \frac{4 x ^{3} y}{1 - x ^{2}} = 1

y = - \frac{x ^{3}}{3 ( 1 - x ^{4} )} + \frac{x}{1 - x ^{4}} + \frac{c _{1}}{1 - x ^{4}}

解答ステップ

(1 + x^{2}) \frac{d y}{d x} - \frac{4 x ^{3} y}{1 - x ^{2}} = 1

線形 ODE を解く:

y = - \frac{x ^{3}}{3 ( 1 - x ^{4} )} + \frac{x}{1 - x ^{4}} + \frac{c _{1}}{1 - x ^{4}}

y = - \frac{x ^{3}}{3 ( 1 - x ^{4} )} + \frac{x}{1 - x ^{4}} + \frac{c _{1}}{1 - x ^{4}}