(dP)/(dt)=8sqrt(Pt),P(1)=7

Lösung

\frac{d P}{d t} = 8 Pt, P (1) = 7

P = \frac{64}{9} - \frac{16 7}{3} + \frac{64 t ^{3}}{9} - \frac{128 t ^{\frac{3}{2}}}{9} + \frac{16 7 t ^{\frac{3}{2}}}{3} + 7

Schritte zur Lösung

\frac{d P}{d t} = 8 Pt

Solve separable ODE:

P = \frac{64}{9} - \frac{16 7}{3} + \frac{64 t ^{3}}{9} - \frac{128 t ^{\frac{3}{2}}}{9} + \frac{16 7 t ^{\frac{3}{2}}}{3} + 7

P = \frac{64}{9} - \frac{16 7}{3} + \frac{64 t ^{3}}{9} - \frac{128 t ^{\frac{3}{2}}}{9} + \frac{16 7 t ^{\frac{3}{2}}}{3} + 7

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

\frac{d}{d θ} (r (θ)) r (θ) = \frac{3}{17 - θ}

\frac{d x}{d t} = 75 - \frac{x}{100}, x = 4000, t = 0

(2 y - 2) \frac{d y}{d x} = 3 x^{2} + 4 x + 2, y (1) = - 2

d s + cos (2 t) d t = 0