(dP)/(dt)=8sqrt(Pt)

Lösung

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

P = \frac{64 t ^{3}}{9} + \frac{8 c _{1} t ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

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

Solve separable ODE:

P = \frac{64 t ^{3}}{9} + \frac{8 c _{1} t ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

P = \frac{64 t ^{3}}{9} + \frac{8 c _{1} t ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

\frac{d x}{d t} = 60 - \frac{x}{100}, x = 5000, t = 0

y^{^{'}} - \frac{2 y}{x} = 0

y^{^{'}} = 4 y, y (0) = 1

\frac{d y}{d x} = \frac{y}{x ^{2} - 1}

2 y + 3 + (2 x - 1) \frac{d y}{d x} = 0