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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + 9 y = 0

y = x^{4} + 4 x^{2} - x, (1, 4)

y = \frac{1}{3} x^{3} - 3 x^{2} + 5 x

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

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