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Beliebt Rechnen >

(dp)/(dt)=4sqrt(pt),p(1)=3

Lösung

\frac{d p}{d t} = 4 pt, p (1) = 3

Lösung

p = \frac{16}{9} - \frac{8}{3} + \frac{16 t ^{3}}{9} - \frac{32 t ^{\frac{3}{2}}}{9} + \frac{8 t ^{\frac{3}{2}}}{3} + 3

Schritte zur Lösung

\frac{d p}{d t} = 4 pt

Solve separable ODE:

p = \frac{16}{9} - \frac{8}{3} + \frac{16 t ^{3}}{9} - \frac{32 t ^{\frac{3}{2}}}{9} + \frac{8 t ^{\frac{3}{2}}}{3} + 3

p = \frac{16}{9} - \frac{8}{3} + \frac{16 t ^{3}}{9} - \frac{32 t ^{\frac{3}{2}}}{9} + \frac{8 t ^{\frac{3}{2}}}{3} + 3

Graph

Beliebte Beispiele

y - 4 y^{^{'}} + 11 y = 0

(dy)/(dx)=(x^2+3x-1)/(y^2)

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

y^'-x*e^y=0,y(0)=2

y^{^{'}} - x \cdot e^{y} = 0, y (0) = 2

(dp)/(dt)=4sqrt(pt),p(1)=7

\frac{d p}{d t} = 4 pt, p (1) = 7

y^'=(sin(x))(cos^2(x))(tan(y))

y^{^{'}} = (sin (x)) (cos^{2} (x)) (tan (y))