x(dv)/(dx)=(-v(1+v^2))/(1-v^2)

解

x \frac{d v}{d x} = \frac{- v ( 1 + v ^{2} )}{1 - v ^{2}}

v = \frac{x + x ^{2} - 4 e ^{2 c_{1}}}{2 e ^{c_{1}}}, v = \frac{x - x ^{2} - 4 e ^{2 c_{1}}}{2 e ^{c_{1}}}

解答ステップ

x \frac{d v}{d x} = \frac{- v ( 1 + v ^{2} )}{1 - v ^{2}}

分離可能 ODE を解く:

v = \frac{x + x ^{2} - 4 e ^{2 c_{1}}}{2 e ^{c_{1}}}, v = \frac{x - x ^{2} - 4 e ^{2 c_{1}}}{2 e ^{c_{1}}}

v = \frac{x + x ^{2} - 4 e ^{2 c_{1}}}{2 e ^{c_{1}}}, v = \frac{x - x ^{2} - 4 e ^{2 c_{1}}}{2 e ^{c_{1}}}