(dP)/(dt)=1.1P(1-P/(5000))

Lösung

\frac{d P}{d t} = 1.1 P (1 - \frac{P}{5000})

P = - \frac{5000 e ^{1.1 t + c_{1}}}{1 - e ^{1.1 t + c_{1}}}

Schritte zur Lösung

\frac{d P}{d t} = 1.1 P (1 - \frac{P}{5000})

Solve separable ODE:

P = - \frac{5000 e ^{1.1 t + c_{1}}}{1 - e ^{1.1 t + c_{1}}}

P = - \frac{5000 e ^{1.1 t + c_{1}}}{1 - e ^{1.1 t + c_{1}}}

x^{^{'}} = x^{2} \cdot \frac{1}{2}

y^{^{'}} + 16 x y = x

\frac{d y}{d x} = y - \frac{y ^{2}}{3}

y^{^{'}} = 12 y - 15

(x - 2) y^{^{'}} - y - 1 = 0