What is the solution for (dV)/(dt)=4kpi((3V)/(4pi))^{2/3} ?

The solution for (dV)/(dt)=4kpi((3V)/(4pi))^{2/3} is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dV)/(dt)=4kpi((3V)/(4pi))^{2/3}

\frac{d V}{d t} = 4 kπ (\frac{3 V}{4 π})^{\frac{2}{3}}

V = \frac{4 π k ^{3} t ^{3}}{3} + \frac{4 ^{\frac{2}{3}} π ^{\frac{2}{3}} c _{1} k ^{2} t ^{2}}{3 ^{\frac{2}{3}}} + \frac{4 ^{\frac{1}{3}} π ^{\frac{1}{3}} c _{1}^{2} k t}{3 \cdot 3 ^{\frac{1}{3}}} + \frac{c _{1}^{3}}{27}

Solution steps

\frac{d V}{d t} = 4 kπ (\frac{3 V}{4 π})^{\frac{2}{3}}

Solve separable ODE:

V = \frac{4 π k ^{3} t ^{3}}{3} + \frac{4 ^{\frac{2}{3}} π ^{\frac{2}{3}} c _{1} k ^{2} t ^{2}}{3 ^{\frac{2}{3}}} + \frac{4 ^{\frac{1}{3}} π ^{\frac{1}{3}} c _{1}^{2} k t}{3 \cdot 3 ^{\frac{1}{3}}} + \frac{c _{1}^{3}}{27}

V = \frac{4 π k ^{3} t ^{3}}{3} + \frac{4 ^{\frac{2}{3}} π ^{\frac{2}{3}} c _{1} k ^{2} t ^{2}}{3 ^{\frac{2}{3}}} + \frac{4 ^{\frac{1}{3}} π ^{\frac{1}{3}} c _{1}^{2} k t}{3 \cdot 3 ^{\frac{1}{3}}} + \frac{c _{1}^{3}}{27}

\frac{d t}{d x} = \frac{( 3000 - x )}{100}

3 x^{^{'}} + 21 x = 0

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

\frac{d y}{d t} y = cos (9 t - 13)

\frac{d y}{d x} + x^{2} y = x^{2}, y = 2, x = 0

What is the solution for (dV)/(dt)=4kpi((3V)/(4pi))^{2/3} ?
The solution for (dV)/(dt)=4kpi((3V)/(4pi))^{2/3} is