(dP)/(dt)=0.7P-0.001P^2

Lösung

\frac{d P}{d t} = 0.7 P - 0.001 P^{2}

P = - \frac{1.80187 E - 10 e ^{- 0.69999 \dots t - 0.69999 \dots c_{1}}}{1 - e ^{- 0.69999 \dots (t + c_{1})}} + \frac{699.99999 \dots}{1 - e ^{- 0.69999 \dots (t + c_{1})}}

Schritte zur Lösung

\frac{d P}{d t} = 0.7 P - 0.001 P^{2}

Solve separable ODE:

P = - \frac{1.80187 E - 10 e ^{- 0.69999 \dots t - 0.69999 \dots c_{1}}}{1 - e ^{- 0.69999 \dots (t + c_{1})}} + \frac{699.99999 \dots}{1 - e ^{- 0.69999 \dots (t + c_{1})}}

P = - \frac{1.80187 E - 10 e ^{- 0.69999 \dots t - 0.69999 \dots c_{1}}}{1 - e ^{- 0.69999 \dots (t + c_{1})}} + \frac{699.99999 \dots}{1 - e ^{- 0.69999 \dots (t + c_{1})}}

(3 x - 3 y^{2} x) d x + (5 y - 5 x^{2} y) d y = 0

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

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

e^{(x + y)} \frac{d y}{d x} = x

y^{^{'}} = y^{2} - 20 y + 100