N^'=r-a(N-b)^2

Lösung

N^{^{'}} = r - a (N - b)^{2}

N (t) = - \frac{b e ^{2 r a t + 2 c_{1} r a}}{1 - e ^{2 r a (t + c_{1})}} - \frac{r e ^{2 r a t + 2 c_{1} r a}}{a ( 1 - e ^{2 r a (t + c_{1})} )} + \frac{b}{1 - e ^{2 r a (t + c_{1})}} - \frac{r}{a ( 1 - e ^{2 r a (t + c_{1})} )}

Schritte zur Lösung

N^{'} (t) = r - a (N (t) - b)^{2}

Solve separable ODE:

N (t) = - \frac{b e ^{2 r a t + 2 c_{1} r a}}{1 - e ^{2 r a (t + c_{1})}} - \frac{r e ^{2 r a t + 2 c_{1} r a}}{a ( 1 - e ^{2 r a (t + c_{1})} )} + \frac{b}{1 - e ^{2 r a (t + c_{1})}} - \frac{r}{a ( 1 - e ^{2 r a (t + c_{1})} )}

N (t) = - \frac{b e ^{2 r a t + 2 c_{1} r a}}{1 - e ^{2 r a (t + c_{1})}} - \frac{r e ^{2 r a t + 2 c_{1} r a}}{a ( 1 - e ^{2 r a (t + c_{1})} )} + \frac{b}{1 - e ^{2 r a (t + c_{1})}} - \frac{r}{a ( 1 - e ^{2 r a (t + c_{1})} )}

y^{^{'}} = \frac{1}{2} y cos^{2} (y)

\frac{d h}{d t} = - \frac{3}{100} h - 19

y^{^{'}} = y (e^{x} - x)

y^{^{'}} = sin (y) tan (y)

y^{^{'}} = 2 e^{- 2 y}