(dp)/(dt)=2sqrt(pt),p(1)=6

Lösung

\frac{d p}{d t} = 2 pt, p (1) = 6

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} + 6

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} + 6

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} + 6

y^{^{'}} + 3 y = 13, y (0) = 0

y^{^{'}} + x^{2} y = 0, y (0) = 2

x^{^{'}} = x \cdot (1 - x)

\frac{d y}{d x} = 16 x y

x y^{^{'}} - y^{^{'}} \cdot ln (x) + y = 0