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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

integral of-x^2+9x

\int - x^{2} + 9 x d x

y^{''}-2y^'-36y=0

y^{^{''}} - 2 y^{^{'}} - 36 y = 0

integral of x/(2x^2+x+3)

\int \frac{x}{2 x ^{2} + x + 3} d x

y^{^{'}} = 3 y, y (0) = 2

integral from 2 to infinity of e^{-x}

\int_{2}^{\infty} e^{- x} d x