10(dv)/(dx)=200-5v^2

解

10 \frac{d v}{d x} = 200 - 5 v^{2}

v = - \frac{2 10 e ^{210 x + 210 c_{1}}}{1 - e ^{210 (x + c_{1})}} - \frac{2 10}{1 - e ^{210 (x + c_{1})}}

解答ステップ

10 \frac{d v}{d x} = 200 - 5 v^{2}

分離可能 ODE を解く:

v = - \frac{2 10 e ^{210 x + 210 c_{1}}}{1 - e ^{210 (x + c_{1})}} - \frac{2 10}{1 - e ^{210 (x + c_{1})}}

v = - \frac{2 10 e ^{210 x + 210 c_{1}}}{1 - e ^{210 (x + c_{1})}} - \frac{2 10}{1 - e ^{210 (x + c_{1})}}