What is the solution for (dy)/(dt)+20 6/5-6/5 e^{-20t}=24 ?

The solution for (dy)/(dt)+20 6/5-6/5 e^{-20t}=24 is y=-3/50 e^{-20t}+c_{1}

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(dy)/(dt)+20 6/5-6/5 e^{-20t}=24

\frac{d y}{d t} + 20 \frac{6}{5} - \frac{6}{5} e^{- 20 t} = 24

y = - \frac{3}{50} e^{- 20 t} + c_{1}

Solution steps

\frac{d y}{d t} + 20 \frac{6}{5} - \frac{6}{5} e^{- 20 t} = 24

Substitute

\frac{d y}{d t}

with

y^{'} (t)

y^{^{'}} (t) + 20 \cdot \frac{6}{5} - \frac{6}{5} e^{- 20 t} = 24

Isolate

y^{'} (t) : y^{'} (t) = \frac{6}{5} e^{- 20 t}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int \frac{6}{5} e^{- 20 t} d t

\int \frac{6}{5} e^{- 20 t} d t = - \frac{3}{50} e^{- 20 t} + c_{1}

y = - \frac{3}{50} e^{- 20 t} + c_{1}

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What is the solution for (dy)/(dt)+20 6/5-6/5 e^{-20t}=24 ?
The solution for (dy)/(dt)+20 6/5-6/5 e^{-20t}=24 is y=-3/50 e^{-20t}+c_{1}