(dP)/(dt)=2sqrt(Pt),P(1)=3

Lösung

\frac{d P}{d t} = 2 Pt, P (1) = 3

P = \frac{4}{9} - \frac{4}{3} + \frac{4 t ^{3}}{9} - \frac{8 t ^{\frac{3}{2}}}{9} + \frac{4 t ^{\frac{3}{2}}}{3} + 3

Schritte zur Lösung

\frac{d P}{d t} = 2 Pt

Solve separable ODE:

P = \frac{4}{9} - \frac{4}{3} + \frac{4 t ^{3}}{9} - \frac{8 t ^{\frac{3}{2}}}{9} + \frac{4 t ^{\frac{3}{2}}}{3} + 3

P = \frac{4}{9} - \frac{4}{3} + \frac{4 t ^{3}}{9} - \frac{8 t ^{\frac{3}{2}}}{9} + \frac{4 t ^{\frac{3}{2}}}{3} + 3

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

3 y^{^{'}} + 2 y = 0

x y^{^{'}} - y = 2

y^{^{'}} = - \frac{3 x ^{2}}{4 y}

y^{^{'}} = y cos (5 x), y (0) = 1