The solution of the differential equation `(e^x+e^(-x))dy-(e^x-e^(-x))dx`=0 is

Explanation

`(e^(x)+e^(-x))dy-(e^(x)-e^(-x))dx=0`
`implies dy=(e^(x)-e^(-x))/(e^(x)+e^(-x))dx`
`implies intdy=int(e^(x)-e^(-x))/(e^(x)+e^(-x))dx+c`
Let `e^(x)+e^(-x)=t`
`implies (e^(x)-e^(-x))dx=dt`
`implies int dy=int(1)/(t)dt+c`
`implies y=logt+c`
`implies y=log(e^(x)+e^(-x))+c`