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=e^{e^t+t+c_{1}}+3

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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 = e^{e^{t} + t + c_{1}} + 3

Solution steps

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

Solve separable ODE:

x = e^{e^{t} + t + c_{1}} + 3

x = e^{e^{t} + t + c_{1}} + 3

\int_{0}^{60} 60 e^{- 0.02 x} d x

(0, - 9), (4, - 10)

6 (6 + \frac{18}{x ^{3}})

\frac{\partial}{\partial y} (e^{- x - y})

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=e^{e^t+t+c_{1}}+3