(dP)/(dt)=0.02P(1-P/(250000))

解答

\frac{d P}{d t} = 0.02 P (1 - \frac{P}{250000})

P = - \frac{250000 e ^{0.02 t + c_{1}}}{1 - e ^{0.02 t + c_{1}}}

求解步骤

\frac{d P}{d t} = 0.02 P (1 - \frac{P}{250000})

求解可分离方程:

P = - \frac{250000 e ^{0.02 t + c_{1}}}{1 - e ^{0.02 t + c_{1}}}

P = - \frac{250000 e ^{0.02 t + c_{1}}}{1 - e ^{0.02 t + c_{1}}}

\frac{d y}{d x} = 4 x (y^{2} + 1)

\frac{d y}{d t} = 4 - y

y^{^{'}} = x + x y

\frac{1 + cos ( 2 x )}{1 + sin ( y )} + \frac{d y}{d x} = 0

(2 x - 1) d x - (3 y - 7) d y = 0