(dP)/(dt)=P(7-P)-49/4

解

\frac{d P}{d t} = P (7 - P) - \frac{49}{4}

P = \frac{1}{t + c _{1}} + \frac{7 t}{2 ( t + c _{1} )} + \frac{7 c _{1}}{2 ( t + c _{1} )}

解答ステップ

\frac{d P}{d t} = P (7 - P) - \frac{49}{4}

分離可能 ODE を解く:

P = \frac{1}{t + c _{1}} + \frac{7 t}{2 ( t + c _{1} )} + \frac{7 c _{1}}{2 ( t + c _{1} )}

P = \frac{1}{t + c _{1}} + \frac{7 t}{2 ( t + c _{1} )} + \frac{7 c _{1}}{2 ( t + c _{1} )}