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Beliebt Rechnen >

((dv)/(dt)+kv(t))e^{kt}=ge^{kt}

Lösung

(\frac{d v}{d t} + k v) e^{k t} = g e^{k t}

Lösung

v = - \frac{e ^{- k t - c_{1}}}{k} + \frac{g}{k}

Schritte zur Lösung

(\frac{d v}{d t} + k v) e^{k t} = g e^{k t}

Solve separable ODE:

v = - \frac{e ^{- k t - c_{1}}}{k} + \frac{g}{k}

v = - \frac{e ^{- k t - c_{1}}}{k} + \frac{g}{k}

Graph

Beliebte Beispiele

y^'(t)=(1+y)(3-y),y(0)=4

y^{^{'}} (t) = (1 + y) (3 - y), y (0) = 4

(dy)/(dx)=0.04-y/(4320/7)

\frac{d y}{d x} = 0.04 - \frac{y}{\frac{4320}{7}}

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

\frac{d y}{d x} = (1 + 2 x) y

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

1 + y^{2} + x y y^{^{'}} = 0