E^y + e^-y =2x or e^2y - 2xe^y + 1 = 0 equation

Main Question or Discussion Point

In this textbook i am looking at it says:

"Thus e^y + e^-y =2x or

e^2y - 2xe^y + 1 = 0"

how did they go from the first to the second part?

Hurkyl
Staff Emeritus
Gold Member
Well, look at pieces of the equation and see if that gives you any clues.

For example, their second equation has an e^(2y) in it1. Can you think of anything to do to the first equation so that the result will have an e^(2y) in it?

1: I assume you meant e^(2y) and not e^2y (which is the same as (e^2)y)

You should really try to figure this out yourself. What's the difference between the two equations?

i still dont get how to go from

$$e^y + exp(-y)=2x$$

to

$$e^2y - 2xe^y + 1 = 0$$