(dx)/(dt)=c_{1}x-c_{2}x^2

解

\frac{d x}{d t} = c_{1} x - c_{2} x^{2}

x = \frac{c _{1} e ^{c_{1} t + c_{1} c_{1}}}{c _{2} ( - 1 + e ^{c_{1} (t + c_{1})} )}

解答ステップ

\frac{d x}{d t} = c_{1} x - c_{2} x^{2}

分離可能 ODE を解く:

x = \frac{c _{1} e ^{c_{1} t + c_{1} c_{1}}}{c _{2} ( - 1 + e ^{c_{1} (t + c_{1})} )}

x = \frac{c _{1} e ^{c_{1} t + c_{1} c_{1}}}{c _{2} ( - 1 + e ^{c_{1} (t + c_{1})} )}