What is the solution for (dx)/(dt)+xe^t=1-x ?

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

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(dx)/(dt)+xe^t=1-x

\frac{d x}{d t} + x e^{t} = 1 - x

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

Solution steps

\frac{d x}{d t} + x e^{t} = 1 - x

Solve linear ODE:

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

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

(5, - 6), (8, - 4)

x \to 0 lim (1 - 3 x)

x y^{^{'}} + \frac{1}{2} y = x

\frac{\partial}{\partial x} (ln (x^{4} y))

\frac{d}{d x} (x sinh (x) - 6 cosh (x))

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