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Beliebt Rechnen >

(dP)/(dt)=7sqrt(Pt),P(1)=6

Lösung

\frac{d P}{d t} = 7 Pt, P (1) = 6

Lösung

P = \frac{49}{9} - \frac{14 2}{3} + \frac{49 t ^{3}}{9} - \frac{98 t ^{\frac{3}{2}}}{9} + \frac{14 2 t ^{\frac{3}{2}}}{3} + 6

Schritte zur Lösung

\frac{d P}{d t} = 7 Pt

Solve separable ODE:

P = \frac{49}{9} - \frac{14 2}{3} + \frac{49 t ^{3}}{9} - \frac{98 t ^{\frac{3}{2}}}{9} + \frac{14 2 t ^{\frac{3}{2}}}{3} + 6

P = \frac{49}{9} - \frac{14 2}{3} + \frac{49 t ^{3}}{9} - \frac{98 t ^{\frac{3}{2}}}{9} + \frac{14 2 t ^{\frac{3}{2}}}{3} + 6

Graph

Beliebte Beispiele

3 y d x + x d y = 0

v^'=sqrt(2v),v(0)=3.2

v^{^{'}} = 2 v, v (0) = 3.2

sqrt(1-y^2dx)=(1+x^2)ydy

1 - y^{2} d x = (1 + x^{2}) y d y

(dx)/(dt)=e^x*t*cos(t)

\frac{d x}{d t} = e^{x} \cdot t \cdot cos (t)

y^'=(4ty)/(2+t^2),y(0)=4

y^{^{'}} = \frac{4 t y}{2 + t ^{2}}, y (0) = 4