(dP)/(dt)=0.05P-0.00125P^2

Lösung

\frac{d P}{d t} = 0.05 P - 0.00125 P^{2}

P = \frac{1.41421 E - 11 e ^{- 0.05 t - 0.05 c_{1}}}{1 - e ^{- 0.05 (t + c_{1})}} + \frac{40.00000 \dots}{1 - e ^{- 0.05 (t + c_{1})}}

Schritte zur Lösung

\frac{d P}{d t} = 0.05 P - 0.00125 P^{2}

Solve separable ODE:

P = \frac{1.41421 E - 11 e ^{- 0.05 t - 0.05 c_{1}}}{1 - e ^{- 0.05 (t + c_{1})}} + \frac{40.00000 \dots}{1 - e ^{- 0.05 (t + c_{1})}}

P = \frac{1.41421 E - 11 e ^{- 0.05 t - 0.05 c_{1}}}{1 - e ^{- 0.05 (t + c_{1})}} + \frac{40.00000 \dots}{1 - e ^{- 0.05 (t + c_{1})}}

x^{2} d x = \frac{1}{y ^{2}} d y

y^{^{'}} = x y - 2 x, y (0) = 3

\frac{d y}{d x} = \frac{4 x}{3 y + 1}

y^{^{'}} = x y^{\frac{1}{2}}, y (0) = \frac{1}{16} x^{4}

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