y^'=0.05y(1-y/(4000))

Lösung

y^{^{'}} = 0.05 y (1 - \frac{y}{4000})

y = - \frac{4000 e ^{0.05 t + c_{1}}}{1 - e ^{0.05 t + c_{1}}}

Schritte zur Lösung

y^{'} (t) = 0.05 y (1 - \frac{y}{4000})

Solve separable ODE:

y = - \frac{4000 e ^{0.05 t + c_{1}}}{1 - e ^{0.05 t + c_{1}}}

y = - \frac{4000 e ^{0.05 t + c_{1}}}{1 - e ^{0.05 t + c_{1}}}

(x + \frac{x}{y}) d x - d y = 0

\frac{d y}{d x} y = sin^{3} (cos (9 x))

\frac{d y}{d x} = 85 y x^{16}, y = 4

\frac{1}{x} \frac{d y}{d x} = 2 - 4 y

x^{^{'}} = x - t x - t + 1