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Beliebt Rechnen >

(dP)/(dt)=7sqrt(Pt),P(1)=5

Lösung

\frac{d P}{d t} = 7 Pt, P (1) = 5

Lösung

P = \frac{49}{9} - \frac{14 5}{3} + \frac{49 t ^{3}}{9} - \frac{98 t ^{\frac{3}{2}}}{9} + \frac{14 5 t ^{\frac{3}{2}}}{3} + 5

Schritte zur Lösung

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

Solve separable ODE:

P = \frac{49}{9} - \frac{14 5}{3} + \frac{49 t ^{3}}{9} - \frac{98 t ^{\frac{3}{2}}}{9} + \frac{14 5 t ^{\frac{3}{2}}}{3} + 5

P = \frac{49}{9} - \frac{14 5}{3} + \frac{49 t ^{3}}{9} - \frac{98 t ^{\frac{3}{2}}}{9} + \frac{14 5 t ^{\frac{3}{2}}}{3} + 5

Graph

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