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}}

\int_{0}^{1} x (1 - x)^{2} d x

x \to 0 lim (x (\frac{1}{x}))

x \to 8 lim (\frac{6}{x - 8})

\frac{d}{d x} ((e^{x} + x)^{\frac{1}{x}})

\frac{\partial}{\partial x} (x^{9} y^{6} - x^{8} y^{5})

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)}