x^'=0.1078*(1-x/(105900))x-x

Lösung

x^{^{'}} = 0.1078 \cdot (1 - \frac{x}{105900}) x - x

x = \frac{876474.76808 \dots e ^{- 0.89219 \dots t + 0.89219 \dots c_{1}}}{1 - e ^{0.89219 \dots (- t + c_{1})}}

Schritte zur Lösung

x^{'} (t) = 0.1078 \cdot (1 - \frac{x}{105900}) x - x

Löse nach

t, x^{'} (t) = \frac{d x}{d t} = \frac{1}{\frac{d t}{d x}} = \frac{1}{t ^{^{'}}}

(\frac{1}{t ^{^{^{'}}}}) = 0.1078 (1 - \frac{x}{105900}) x - x

Isoliere

t^{^{'}} : t^{^{'}} = - \frac{105900}{x ( 94483.98 + 0.1078 x )}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

t = \int - \frac{105900}{x ( 94483.98 + 0.1078 x )} d x

\int - \frac{105900}{x ( 94483.98 + 0.1078 x )} d x = - 1.12082 \dots (- ln (\frac{1}{94483.98} (94483.98 + 0.1078 x)) + ln (\frac{1}{94483.98} (94483.98 + 0.1078 x) - 1)) + c_{1}

t = - 1.12082 \dots (- ln (\frac{1}{94483.98} (94483.98 + 0.1078 x)) + ln (\frac{1}{94483.98} (94483.98 + 0.1078 x) - 1)) + c_{1}

Vereinfache

t = - 1.12082 \dots ln (\frac{0.1078 x}{94483.98 + 0.1078 x}) + c_{1}

Isoliere

x : x = \frac{876474.76808 \dots e ^{- 0.89219 \dots t + 0.89219 \dots c_{1}}}{1 - e ^{0.89219 \dots (- t + c_{1})}}

x = \frac{876474.76808 \dots e ^{- 0.89219 \dots t + 0.89219 \dots c_{1}}}{1 - e ^{0.89219 \dots (- t + c_{1})}}

n = 1 \sum \infty \frac{15}{n}

\int_{0}^{1} x e^{2 x} d x

y^{^{'}} + 4 y = 6

d er i v a t i v e - 6.25 t^{2} + 50 t

(x^{2} + 4 x y) d x + x d y = 0