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

[thenewbosco]

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]

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)

 

[Dr Avalanchez]

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

 

[thenewbosco]

i still don't get how to go from

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

to

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

help please

 

[asdf60]

I'm not sure, but that y should be raised too...e^(2y) not (e^2)y

 

[Hurkyl]

Have you tried any of our hints?