What is the solution for (dv)/(dt)=60-9/100*v ?

The solution for (dv)/(dt)=60-9/100*v is v=-(e^{(-9t-c_{1})/(100)})/9+2000/3

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(dv)/(dt)=60-9/100*v

\frac{d v}{d t} = 60 - \frac{9}{100} \cdot v

v = - \frac{e ^{\frac{- 9 t - c _{1}}{100}}}{9} + \frac{2000}{3}

Solution steps

\frac{d v}{d t} = 60 - \frac{9}{100} \cdot v

Solve separable ODE:

v = - \frac{e ^{\frac{- 9 t - c _{1}}{100}}}{9} + \frac{2000}{3}

v = - \frac{e ^{\frac{- 9 t - c _{1}}{100}}}{9} + \frac{2000}{3}

e^{y} y^{^{'}} = \frac{( ln ( t ) ) ^{2}}{t}, y (1) = ln (8)

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

(3 t^{2} + 5) y^{^{'}} = 3 t y, y (0) = 8

\frac{d y}{d x} = \frac{x ^{3}}{y ^{3}}

y^{^{'}} = e^{4 y + 7 t}

What is the solution for (dv)/(dt)=60-9/100*v ?
The solution for (dv)/(dt)=60-9/100*v is v=-(e^{(-9t-c_{1})/(100)})/9+2000/3