What is the solution for (dy)/(dx)=(e^x-1)/(e^y),f(1)=0 ?

The solution for (dy)/(dx)=(e^x-1)/(e^y),f(1)=0 is y=ln(e^x-x+c_{1})

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(dy)/(dx)=(e^x-1)/(e^y),f(1)=0

\frac{d y}{d x} = \frac{e ^{x} - 1}{e ^{y}}, f (1) = 0

y = ln (e^{x} - x + c_{1})

Solution steps

\frac{d y}{d x} = \frac{e ^{x} - 1}{e ^{y}}

Solve separable ODE:

y = ln (e^{x} - x + c_{1})

y = ln (e^{x} - x + c_{1})

7 x

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What is the solution for (dy)/(dx)=(e^x-1)/(e^y),f(1)=0 ?
The solution for (dy)/(dx)=(e^x-1)/(e^y),f(1)=0 is y=ln(e^x-x+c_{1})