What is the solution for y^'+e^xy=1 ?

The solution for y^'+e^xy=1 is y=(\Ei(e^x))/(e^{e^x)}+(c_{1})/(e^{e^x)}

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y^'+e^xy=1

y^{^{'}} + e^{x} y = 1

y = \frac{Ei ( e ^{x} )}{e ^{e^{x}}} + \frac{c _{1}}{e ^{e^{x}}}

Solution steps

y^{'} (x) + e^{x} y = 1

Solve linear ODE:

y = \frac{Ei ( e ^{x} )}{e ^{e^{x}}} + \frac{c _{1}}{e ^{e^{x}}}

y = \frac{Ei ( e ^{x} )}{e ^{e^{x}}} + \frac{c _{1}}{e ^{e^{x}}}

2 x^{^{''}} + 4 x^{^{'}} + 8 x = 0, x (0) = 0, x^{^{'}} (0) = 1

\frac{d}{d θ} (e^{- i θ})

\frac{\partial}{\partial x} (ln (tan (\frac{x}{2})))

\int \frac{1 - x ^{2}}{x} d x

x \to 0 + lim (cos (x))

What is the solution for y^'+e^xy=1 ?
The solution for y^'+e^xy=1 is y=(\Ei(e^x))/(e^{e^x)}+(c_{1})/(e^{e^x)}