What is the solution for xe^y(dy)/(dx)+e^y=e^x ?

The solution for xe^y(dy)/(dx)+e^y=e^x is y=ln((c_{1})/x+(e^x)/x)

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xe^y(dy)/(dx)+e^y=e^x

x e^{y} \frac{d y}{d x} + e^{y} = e^{x}

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

Solution steps

x e^{y} \frac{d y}{d x} + e^{y} = e^{x}

Solve exact ODE:

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

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

What is the solution for xe^y(dy)/(dx)+e^y=e^x ?
The solution for xe^y(dy)/(dx)+e^y=e^x is y=ln((c_{1})/x+(e^x)/x)