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Beliebt Rechnen >

(dx)/(dt)=t^{3/2},x(3)=7

Lösung

\frac{d x}{d t} = t^{\frac{3}{2}}, x (3) = 7

Lösung

x = \frac{2 t ^{\frac{5}{2}}}{5} + 7 - \frac{18 \cdot 3 ^{\frac{1}{2}}}{5}

Schritte zur Lösung

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

Ersetze

\frac{d x}{d t}

mit

x^{'} (t)

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

Wenn

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

dann

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

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

\int t^{\frac{3}{2}} d t = \frac{2}{5} t^{\frac{5}{2}} + c_{1}

x = \frac{2}{5} t^{\frac{5}{2}} + c_{1}

Wende die Anfangsbedingung an:

x = \frac{2 t ^{\frac{5}{2}}}{5} + 7 - \frac{18 \cdot 3 ^{\frac{1}{2}}}{5}

x = \frac{2 t ^{\frac{5}{2}}}{5} + 7 - \frac{18 \cdot 3 ^{\frac{1}{2}}}{5}

Graph

Beliebte Beispiele

derivative of 6x^{-1/2}

\frac{d}{d x} (6 x^{- \frac{1}{2}})

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t an g e n t y = 2 x^{2} + \frac{3}{x}

(dy)/(dx)+y/x = 1/(x^2)

\frac{d y}{d x} + \frac{y}{x} = \frac{1}{x ^{2}}

integral of e^{-4x+pi}

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