What is the solution for (dy)/(dx)=(e^y+1)/(e^y) ?

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

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(dy)/(dx)=(e^y+1)/(e^y)

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

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

Solution steps

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

Solve separable ODE:

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

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

x = - 2, x = 1, y = 2 x^{2} + 7, y = 0

y^{^{'}} + 2 x y = 2 x e^{- x^{2}}

x \to 0 lim (\frac{x + 1}{x})

\int_{1}^{3} \frac{2}{x ^{3}} d x

\int \frac{x ^{n - 1}}{a + b x ^{n}} d x

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