What is the solution for v^'=9.8-3/2 v,v(0)=1.5 ?

The solution for v^'=9.8-3/2 v,v(0)=1.5 is v(t)=-(e^{-1.49999…t+2.02154…})/(1.5)+(9.8)/(1.5)

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v^'=9.8-3/2 v,v(0)=1.5

v^{^{'}} = 9.8 - \frac{3}{2} v, v (0) = 1.5

v (t) = - \frac{e ^{- 1.49999 \dots t + 2.02154 \dots}}{1.5} + \frac{9.8}{1.5}

Solution steps

v^{'} (t) = 9.8 - \frac{3}{2} v (t)

Solve separable ODE:

v (t) = - \frac{e ^{- 1.49999 \dots t + 2.02154 \dots}}{1.5} + \frac{9.8}{1.5}

v (t) = - \frac{e ^{- 1.49999 \dots t + 2.02154 \dots}}{1.5} + \frac{9.8}{1.5}

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What is the solution for v^'=9.8-3/2 v,v(0)=1.5 ?
The solution for v^'=9.8-3/2 v,v(0)=1.5 is v(t)=-(e^{-1.49999…t+2.02154…})/(1.5)+(9.8)/(1.5)