What is the solution for (dv)/(dt)=9.6138-8v ?

The solution for (dv)/(dt)=9.6138-8v is v=-(e^{-8t-c_{1}})/8+(9.6138)/8

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(dv)/(dt)=9.6138-8v

\frac{d v}{d t} = 9.6138 - 8 v

v = - \frac{e ^{- 8 t - c_{1}}}{8} + \frac{9.6138}{8}

Solution steps

\frac{d v}{d t} = 9.6138 - 8 v

Solve separable ODE:

v = - \frac{e ^{- 8 t - c_{1}}}{8} + \frac{9.6138}{8}

v = - \frac{e ^{- 8 t - c_{1}}}{8} + \frac{9.6138}{8}

\frac{d y}{d x} = - \frac{3 x + x y ^{2}}{2 y + x ^{2} y}

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

y^{^{'}} = \frac{11 x ^{2} - 1}{11 + 3 y}

\frac{d y}{d x} = \frac{cos ( x ) y}{2}

y^{^{'}} = e^{- y} cos (t), y (\frac{π}{6}) = 1

What is the solution for (dv)/(dt)=9.6138-8v ?
The solution for (dv)/(dt)=9.6138-8v is v=-(e^{-8t-c_{1}})/8+(9.6138)/8