What is the solution for (dv)/(dt)=32.2-1/40 v ?

The solution for (dv)/(dt)=32.2-1/40 v is v=-40e^{(-t-c_{1})/(40)}+1288

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(dv)/(dt)=32.2-1/40 v

\frac{d v}{d t} = 32.2 - \frac{1}{40} v

v = - 40 e^{\frac{- t - c _{1}}{40}} + 1288

Solution steps

\frac{d v}{d t} = 32.2 - \frac{1}{40} v

Solve separable ODE:

v = - 40 e^{\frac{- t - c _{1}}{40}} + 1288

v = - 40 e^{\frac{- t - c _{1}}{40}} + 1288

\frac{d P}{d t} = (0.1) P - (0.05) P (t)^{2}

y^{^{'}} = \frac{2 ( 1 + x )}{x y}

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

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

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

What is the solution for (dv)/(dt)=32.2-1/40 v ?
The solution for (dv)/(dt)=32.2-1/40 v is v=-40e^{(-t-c_{1})/(40)}+1288