What is the solution for (dv)/(dt)=1-0.4v ?

The solution for (dv)/(dt)=1-0.4v is v=-(5e^{(-2t-c_{1})/5})/(2)+5/2

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(dv)/(dt)=1-0.4v

\frac{d v}{d t} = 1 - 0.4 v

v = - \frac{5 e ^{\frac{- 2 t - c _{1}}{5}}}{2} + \frac{5}{2}

Solution steps

\frac{d v}{d t} = 1 - 0.4 v

Solve separable ODE:

v = - \frac{5 e ^{\frac{- 2 t - c _{1}}{5}}}{2} + \frac{5}{2}

v = - \frac{5 e ^{\frac{- 2 t - c _{1}}{5}}}{2} + \frac{5}{2}

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

(3 x^{2} y^{2} - 10 x y^{2}) d x + (2 x^{3} y - 10 x^{2} y) d y = 0

y^{^{'}} + 12 x y = - x

x^{2} sin (x) d x + x y d y = 0

\frac{d y}{d x} - 4 x y = x

What is the solution for (dv)/(dt)=1-0.4v ?
The solution for (dv)/(dt)=1-0.4v is v=-(5e^{(-2t-c_{1})/5})/(2)+5/2