What is the solution for (dy)/(dx)=(e^x)/(9+e^x) ?

The solution for (dy)/(dx)=(e^x)/(9+e^x) is y=ln(9+e^x)+c_{1}

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(dy)/(dx)=(e^x)/(9+e^x)

\frac{d y}{d x} = \frac{e ^{x}}{9 + e ^{x}}

y = ln (9 + e^{x}) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{e ^{x}}{9 + e ^{x}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{e ^{x}}{9 + e ^{x}}

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

then

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

y = \int \frac{e ^{x}}{9 + e ^{x}} d x

\int \frac{e ^{x}}{9 + e ^{x}} d x = ln (9 + e^{x}) + c_{1}

y = ln (9 + e^{x}) + c_{1}

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

x \to \frac{x}{6} lim (cot (x))

y = x^{2} + 5 x

16 x, \frac{4}{x}, \frac{1}{4} x

\int \frac{sin ( x )}{4 - cos ( x )} d x

What is the solution for (dy)/(dx)=(e^x)/(9+e^x) ?
The solution for (dy)/(dx)=(e^x)/(9+e^x) is y=ln(9+e^x)+c_{1}