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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

(1-x)(dy)/(dx)=y^2

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

y^'=(1-2x)/y ,y(1)=-2

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

(dy)/(dx)=3x^2y,y(0)=2

\frac{d y}{d x} = 3 x^{2} y, y (0) = 2

y^'=\sqrt[3]{y}

y^{^{'}} = 3 y

tan(x)sec(y)dx-tan(y)sec(x)dy=0

tan (x) sec (y) d x - tan (y) sec (x) d y = 0