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Beliebt Rechnen >

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

Lösung

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

Lösung

P = \frac{1}{9} + \frac{t ^{3}}{9} - \frac{2 7}{3} - \frac{2 t ^{\frac{3}{2}}}{9} + \frac{2 7 t ^{\frac{3}{2}}}{3} + 7

Schritte zur Lösung

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

Solve separable ODE:

P = \frac{1}{9} + \frac{t ^{3}}{9} - \frac{2 7}{3} - \frac{2 t ^{\frac{3}{2}}}{9} + \frac{2 7 t ^{\frac{3}{2}}}{3} + 7

P = \frac{1}{9} + \frac{t ^{3}}{9} - \frac{2 7}{3} - \frac{2 t ^{\frac{3}{2}}}{9} + \frac{2 7 t ^{\frac{3}{2}}}{3} + 7

Graph

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