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人気のある微分積分 >

(dx)/(dt)=x^2-3

解

\frac{d x}{d t} = x^{2} - 3

解

x = \frac{3 e ^{23 c_{1}}}{e ^{23 t} - e ^{23 c_{1}}} + \frac{3 e ^{23 t}}{e ^{23 t} - e ^{23 c_{1}}}

解答ステップ

\frac{d x}{d t} = x^{2} - 3

代用

\frac{d x}{d t}

と

x^{'} (t)

x^{^{'}} (t) = x^{2} - 3

t

を解く

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

(\frac{1}{t ^{^{^{'}}}}) = x^{2} - 3

分離する

t^{^{'}} : t^{^{'}} = \frac{1}{x ^{2} - 3}

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

であれば

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

t = \int \frac{1}{x ^{2} - 3} d x

\int \frac{1}{x ^{2} - 3} d x = - \frac{1}{2 3} (ln (\frac{x}{3} + 1) - ln (\frac{x}{3} - 1)) + c_{1}

t = - \frac{1}{2 3} (ln (\frac{x}{3} + 1) - ln (\frac{x}{3} - 1)) + c_{1}

分離する

x : x = \frac{3 e ^{23 c_{1}}}{e ^{23 t} - e ^{23 c_{1}}} + \frac{3 e ^{23 t}}{e ^{23 t} - e ^{23 c_{1}}}

x = \frac{3 e ^{23 c_{1}}}{e ^{23 t} - e ^{23 c_{1}}} + \frac{3 e ^{23 t}}{e ^{23 t} - e ^{23 c_{1}}}

グラフ

人気の例

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