(dv)/(dt)=v^{(2/3)}

Lösung

\frac{d v}{d t} = v^{(\frac{2}{3})}

v = \frac{t ^{3}}{27} + \frac{c _{1} t ^{2}}{9} + \frac{c _{1}^{2} t}{9} + \frac{c _{1}^{3}}{27}

Schritte zur Lösung

\frac{d v}{d t} = v^{(\frac{2}{3})}

Solve separable ODE:

v = \frac{t ^{3}}{27} + \frac{c _{1} t ^{2}}{9} + \frac{c _{1}^{2} t}{9} + \frac{c _{1}^{3}}{27}

v = \frac{t ^{3}}{27} + \frac{c _{1} t ^{2}}{9} + \frac{c _{1}^{2} t}{9} + \frac{c _{1}^{3}}{27}

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

\frac{d y}{d t} = 2 y, y (9) = 4

\frac{d y}{d x} = \frac{2 y}{x} + \frac{y ^{2}}{x}

\frac{d P}{d t} = 1.1 P (1 - \frac{P}{5000})

x^{^{'}} = x^{2} \cdot \frac{1}{2}