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

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

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

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

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

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

\int \frac{e ^{x}}{1 + e ^{x}} d x = ln (1 + e^{x}) + c_{1}

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

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