What is the solution for (dy)/(dx)=(e^x)/(8+e^x) ?

The solution for (dy)/(dx)=(e^x)/(8+e^x) is y=ln(8+e^x)+c_{1}

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(dy)/(dx)=(e^x)/(8+e^x)

\frac{d y}{d x} = \frac{e ^{x}}{8 + e ^{x}}

y = ln (8 + e^{x}) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{e ^{x}}{8 + e ^{x}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{e ^{x}}{8 + e ^{x}}

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

then

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

y = \int \frac{e ^{x}}{8 + e ^{x}} d x

\int \frac{e ^{x}}{8 + e ^{x}} d x = ln (8 + e^{x}) + c_{1}

y = ln (8 + e^{x}) + c_{1}

\frac{d}{d x} (e^{6 x^{2}})

\int_{0}^{5} \frac{1}{x ^{\frac{14}{15}}} d x

x^{^{''}} - 4 x = 0

\int sin (t) \cdot t d t

x \to 2 lim (x^{2} + 8 x - 2)

What is the solution for (dy)/(dx)=(e^x)/(8+e^x) ?
The solution for (dy)/(dx)=(e^x)/(8+e^x) is y=ln(8+e^x)+c_{1}