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Beliebt Rechnen >

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

Lösung

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

Lösung

p = \frac{16}{9} - \frac{8 7}{3} + \frac{16 t ^{3}}{9} - \frac{32 t ^{\frac{3}{2}}}{9} + \frac{8 7 t ^{\frac{3}{2}}}{3} + 7

Schritte zur Lösung

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

Solve separable ODE:

p = \frac{16}{9} - \frac{8 7}{3} + \frac{16 t ^{3}}{9} - \frac{32 t ^{\frac{3}{2}}}{9} + \frac{8 7 t ^{\frac{3}{2}}}{3} + 7

p = \frac{16}{9} - \frac{8 7}{3} + \frac{16 t ^{3}}{9} - \frac{32 t ^{\frac{3}{2}}}{9} + \frac{8 7 t ^{\frac{3}{2}}}{3} + 7

Graph

Beliebte Beispiele

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

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

(dy)/(dx)=y(-8-y)

\frac{d y}{d x} = y (- 8 - y)

(y^2+2)dx+3*x*ydy=0

(y^{2} + 2) d x + 3 \cdot x \cdot y d y = 0

f^'(t)-f(t)=2,f(0)=0

f^{^{'}} (t) - f (t) = 2, f (0) = 0

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