What is the solution for 1/3 ((dx)/(dt))-2e^{-t}=-x ?

The solution for 1/3 ((dx)/(dt))-2e^{-t}=-x is x= 3/(e^t)+(c_{1})/(e^{3t)}

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1/3 ((dx)/(dt))-2e^{-t}=-x

\frac{1}{3} (\frac{d x}{d t}) - 2 e^{- t} = - x

x = \frac{3}{e ^{t}} + \frac{c _{1}}{e ^{3 t}}

Solution steps

\frac{1}{3} (\frac{d x}{d t}) - 2 e^{- t} = - x

Solve linear ODE:

x = \frac{3}{e ^{t}} + \frac{c _{1}}{e ^{3 t}}

x = \frac{3}{e ^{t}} + \frac{c _{1}}{e ^{3 t}}

What is the solution for 1/3 ((dx)/(dt))-2e^{-t}=-x ?
The solution for 1/3 ((dx)/(dt))-2e^{-t}=-x is x= 3/(e^t)+(c_{1})/(e^{3t)}