(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Doing a DE and need to solve for y, just wondering about this particular case.

2. Relevant equations

ln ((2y-1)/(y-1)) = x for y

3. The attempt at a solution

Wolfram says the result is: http://www.wolframalpha.com/input/?i=solve+ln+((2y-1)/(y-1))+=+x+for+y"

How/why did the y and e^x switch places? I know the first step is to exponentiate to get rid of the ln yielding (2y-1)/(y-1) = e^x, but why the heck would you just switch the y's with the e^x after that? Is it because the graph has symmetry over the y=x line? That's all I can figure. If that is the case, how can you tell this is true offhand?

http://www.wolframalpha.com/input/?i=graph+y+=+(e^x-1)/(e^x-2)"

http://www.wolframalpha.com/input/?i=graph+(2y-1)/(y-1)+=+e^x"

Thanks!

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# Homework Help: Solving for y

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