What is the solution for (dx)/(dt)=xe^t+3e^t+x-3 ?

The solution for (dx)/(dt)=xe^t+3e^t+x-3 is x=(6\Ei(-e^t))/(e^{-e^t-t)}+3+(c_{1})/(e^{-e^t-t)}

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(dx)/(dt)=xe^t+3e^t+x-3

\frac{d x}{d t} = x e^{t} + 3 e^{t} + x - 3

x = \frac{6 Ei ( - e ^{t} )}{e ^{- e^{t} - t}} + 3 + \frac{c _{1}}{e ^{- e^{t} - t}}

Solution steps

\frac{d x}{d t} = x e^{t} + 3 e^{t} + x - 3

Solve linear ODE:

x = \frac{6 Ei ( - e ^{t} )}{e ^{- e^{t} - t}} + 3 + \frac{c _{1}}{e ^{- e^{t} - t}}

x = \frac{6 Ei ( - e ^{t} )}{e ^{- e^{t} - t}} + 3 + \frac{c _{1}}{e ^{- e^{t} - t}}

What is the solution for (dx)/(dt)=xe^t+3e^t+x-3 ?
The solution for (dx)/(dt)=xe^t+3e^t+x-3 is x=(6\Ei(-e^t))/(e^{-e^t-t)}+3+(c_{1})/(e^{-e^t-t)}