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

Lösung

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

P = \frac{49}{9} - \frac{14 7}{3} + \frac{49 t ^{3}}{9} - \frac{98 t ^{\frac{3}{2}}}{9} + \frac{14 7 t ^{\frac{3}{2}}}{3} + 7

Schritte zur Lösung

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

Solve separable ODE:

P = \frac{49}{9} - \frac{14 7}{3} + \frac{49 t ^{3}}{9} - \frac{98 t ^{\frac{3}{2}}}{9} + \frac{14 7 t ^{\frac{3}{2}}}{3} + 7

P = \frac{49}{9} - \frac{14 7}{3} + \frac{49 t ^{3}}{9} - \frac{98 t ^{\frac{3}{2}}}{9} + \frac{14 7 t ^{\frac{3}{2}}}{3} + 7

\frac{d y}{d x} = 6 4 x y

\frac{d y}{d t} = cos^{2} (y)

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

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

\frac{d y}{d x} = \frac{( y ln ( x ) )}{x}