(dx)/(dt)=5-(3x)/(1000+2x)

解

\frac{d x}{d t} = 5 - \frac{3 x}{1000 + 2 x}

x = - \frac{1500 W ( - \frac{1}{1500 e ^{\frac{49 t + c _{1}}{3000}}} )}{7} - \frac{5000}{7}

解答ステップ

\frac{d x}{d t} = 5 - \frac{3 x}{1000 + 2 x}

分離可能 ODE を解く:

x = - \frac{1500 W ( - \frac{1}{1500 e ^{\frac{49 t + c _{1}}{3000}}} )}{7} - \frac{5000}{7}

x = - \frac{1500 W ( - \frac{1}{1500 e ^{\frac{49 t + c _{1}}{3000}}} )}{7} - \frac{5000}{7}