(dv)/(dt)=(\sqrt[3]{v})

Lösung

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

v = \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}, v = - \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}

Schritte zur Lösung

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

Solve separable ODE:

v = \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}, v = - \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}

v = \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}, v = - \frac{2 2 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{3 3}

\frac{d y}{d x} = 90 y x^{9}

\frac{d y}{d t} + y cos (t) = 0

y^{^{'}} = - 1 - y^{2}

y^{^{'}} - 4 y = 12

\frac{a ^{3} y}{a x ^{3}} - 21 \frac{d y}{d x} - 20 y = 0