(dh)/(dt)=-3/100 sqrt(h-18)

Lösung

\frac{d h}{d t} = - \frac{3}{100} h - 18

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 18

Schritte zur Lösung

\frac{d h}{d t} = - \frac{3}{100} h - 18

Solve separable ODE:

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 18

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 18

x y^{2} y^{^{'}} = x + 5

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

\frac{d P}{d t} = 0.1 P (1 - \frac{P}{40})

y^{^{'}} = - 4 y + 2

\frac{d y}{d x} + 12 x y = - x