(dy)/(dx)+(xy)/(1-x^2)=(xy^2)/(1-x^2)

解

\frac{d y}{d x} + \frac{x y}{1 - x ^{2}} = \frac{x y ^{2}}{1 - x ^{2}}

y = \frac{1 - x ^{2} + e ^{c_{1}} ( 1 - x ^{2} ) ^{\frac{1}{2}}}{- x ^{2} + 1 - e ^{2 c_{1}}}

解答ステップ

\frac{d y}{d x} + \frac{x y}{1 - x ^{2}} = \frac{x y ^{2}}{1 - x ^{2}}

分離可能 ODE を解く:

y = \frac{1 - x ^{2} + e ^{c_{1}} ( 1 - x ^{2} ) ^{\frac{1}{2}}}{- x ^{2} + 1 - e ^{2 c_{1}}}

y = \frac{1 - x ^{2} + e ^{c_{1}} ( 1 - x ^{2} ) ^{\frac{1}{2}}}{- x ^{2} + 1 - e ^{2 c_{1}}}