What is the solution for (dv)/(dt)=9.81-10v,v(0)=0 ?

The solution for (dv)/(dt)=9.81-10v,v(0)=0 is v=-(981e^{-10t})/(1000)+981/1000

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(dv)/(dt)=9.81-10v,v(0)=0

\frac{d v}{d t} = 9.81 - 10 v, v (0) = 0

v = - \frac{981 e ^{- 10 t}}{1000} + \frac{981}{1000}

Solution steps

\frac{d v}{d t} = 9.81 - 10 v

Solve separable ODE:

v = - \frac{981 e ^{- 10 t}}{1000} + \frac{981}{1000}

v = - \frac{981 e ^{- 10 t}}{1000} + \frac{981}{1000}

y^{3} \frac{d y}{d x} = 2 x^{4} y^{4} - 4 x^{4}

x^{3} \frac{d y}{d x} - sin (x) y = 0

y^{^{'}} = \frac{x ^{2} - 3}{y ^{2}}, y (0) = 4

y^{^{'}} = \frac{x ^{2} - 3}{y ^{2}}, y (0) = 6

\frac{d y}{d x} = 6 + 18 x + 7 y + 21 x y

What is the solution for (dv)/(dt)=9.81-10v,v(0)=0 ?
The solution for (dv)/(dt)=9.81-10v,v(0)=0 is v=-(981e^{-10t})/(1000)+981/1000