How to you find the general solution of dy/dx=e^x/(1+e^x)?

Nov 12, 2016

Use the separation of variables method and then integrate.

Explanation:

Given: $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{e}^{x}}{1 + {e}^{x}}$

Use the separation of variables method:

$\mathrm{dy} = \frac{{e}^{x}}{1 + {e}^{x}} \mathrm{dx}$

Integrate both sides:

$\int \mathrm{dy} = \int \frac{{e}^{x}}{1 + {e}^{x}} \mathrm{dx}$

$y = \ln \left(1 + {e}^{x}\right) + C$