What is the solution for (dv)/(dt)=sqrt(2/9 v) ?

The solution for (dv)/(dt)=sqrt(2/9 v) is v=(t^2}{18}+(c_{1}t)/(3sqrt(2))+\frac{c_{1}^2)/4

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(dv)/(dt)=sqrt(2/9 v)

\frac{d v}{d t} = \frac{2}{9} v

v = \frac{t ^{2}}{18} + \frac{c _{1} t}{3 2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d v}{d t} = \frac{2}{9} v

Solve separable ODE:

v = \frac{t ^{2}}{18} + \frac{c _{1} t}{3 2} + \frac{c _{1}^{2}}{4}

v = \frac{t ^{2}}{18} + \frac{c _{1} t}{3 2} + \frac{c _{1}^{2}}{4}

\frac{d y}{d x} = 4 cos (x) sec (y)

y^{^{'}} = \frac{x}{y + 1}

\frac{d y}{d x} = 5 x^{2} y, y > 0

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

y^{^{'}} = \frac{x ^{2} - 8}{y ^{2}}, y (0) = 2

What is the solution for (dv)/(dt)=sqrt(2/9 v) ?
The solution for (dv)/(dt)=sqrt(2/9 v) is v=(t^2}{18}+(c_{1}t)/(3sqrt(2))+\frac{c_{1}^2)/4