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

解答

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

解答

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

求解步骤

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

求解

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

整理

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

若

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

则

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}

化简

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

整理

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})}}

作图

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