What is the solution for (dv)/(dt)=30-9/100 v ?

The solution for (dv)/(dt)=30-9/100 v is v=-(e^{(-9t-c_{1})/(100)})/9+1000/3

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(dv)/(dt)=30-9/100 v

\frac{d v}{d t} = 30 - \frac{9}{100} v

v = - \frac{e ^{\frac{- 9 t - c _{1}}{100}}}{9} + \frac{1000}{3}

Solution steps

\frac{d v}{d t} = 30 - \frac{9}{100} v

Solve separable ODE:

v = - \frac{e ^{\frac{- 9 t - c _{1}}{100}}}{9} + \frac{1000}{3}

v = - \frac{e ^{\frac{- 9 t - c _{1}}{100}}}{9} + \frac{1000}{3}

2 (x - 1) d x + 3 y^{2} d y = 0, y (2) = 1

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

\frac{d y}{d t} = t^{2} (1 + y^{2})

\frac{d y}{d x} = \frac{( 2 - x )}{( y - 1 )}

\frac{d v}{d t} = g - \frac{1}{40} v

What is the solution for (dv)/(dt)=30-9/100 v ?
The solution for (dv)/(dt)=30-9/100 v is v=-(e^{(-9t-c_{1})/(100)})/9+1000/3