(dp)/(dt)=0.25p(1-p*10^{-4})

Lösung

\frac{d p}{d t} = 0.25 p (1 - p \cdot 1 0^{- 4})

p = - \frac{10000 e ^{0.25 t + c_{1}}}{1 - e ^{0.25 t + c_{1}}}

Schritte zur Lösung

\frac{d p}{d t} = 0.25 p (1 - p \cdot 1 0^{- 4})

Solve separable ODE:

p = - \frac{10000 e ^{0.25 t + c_{1}}}{1 - e ^{0.25 t + c_{1}}}

p = - \frac{10000 e ^{0.25 t + c_{1}}}{1 - e ^{0.25 t + c_{1}}}

- y^{^{'}} - y = 0

\frac{d y}{d x} = \frac{y}{3 x - 1}

4 y y^{^{'}} = x, y (4) = 9

y^{^{'}} = y^{2} - 3 y + 2

\frac{d y}{d x} y = 6 u - 5, u = (\frac{1}{3}) x^{7}