Question

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

Answer 1

Use the separation of variables method and then integrate.

Explanation:

Given: `dy/dx = (e^x)/(1 + e^x)`

Use the separation of variables method:

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

Integrate both sides:

`intdy = int(e^x)/(1 + e^x)dx`

`y = ln( 1 + e^x) + C`