# Why can you Take out An E^xy?

by bmed90
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 P: 99 1. The problem statement, all variables and given/known data Im learning about implicit solutions for differential equations. Anyways I took the derivative of a relation containing x and y to get dy/dy=1-e^xy(y)/ e^xy(x)+1 2. Relevant equations Anywhoo it turns out to be a solution to the diff eq dy/dy = e^-xy - y/ e^-xy + x 3. The attempt at a solution Apparently you can take out an e^xy from dy/dy=1-e^xy(y)/ e^xy(x)+1 in order to get to dy/dy = e^-xy - y/ e^-xy + x How exactly is this so? How does this work....I hope you understand my question
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 Quote by bmed90 1. The problem statement, all variables and given/known data Im learning about implicit solutions for differential equations. Anyways I took the derivative of a relation containing x and y to get dy/dy=1-e^xy(y)/ e^xy(x)+1 2. Relevant equations Anywhoo it turns out to be a solution to the diff eq dy/dy = e^-xy - y/ e^-xy + x 3. The attempt at a solution Apparently you can take out an e^xy from dy/dy=1-e^xy(y)/ e^xy(x)+1 in order to get to dy/dy = e^-xy - y/ e^-xy + x How exactly is this so? How does this work....I hope you understand my question
In order for your question to be understood (without a lot of guessing by the reader) you really need to include parentheses where they're needed so that your mathematical expressions are unambiguous.

What is to be included in you numerators?

What is to be included in you denominators?

etc. ...
P: 361
 Quote by bmed90 dy/dy=1-e^xy(y)/ e^xy(x)+1
dy/dy = 1. Always.

Assuming you mean dy/dx - I'll echo SammyS, who just posted while I was typing, and ask for more clarity. And it wouldn't hurt to post the original xy-relation, either.

 P: 99 Why can you Take out An E^xy? Alright So Basically I just want to know how one goes from this dy/dy= 1-(e^xy)(y)/ (e^xy)(x)+1 to this dy/dy = (e^-xy) - y/ (e^-xy) + x by taking out an e^xy from the top and bottom
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 Quote by bmed90 Alright So Basically I just want to know how one goes from this dy/dy= 1-(e^xy)(y)/ (e^xy)(x)+1 to this dy/dy = (e^-xy) - y/ (e^-xy) + x by taking out an e^xy from the top and bottom
Taking your parentheses literally you have:

dy/dy= 1-(e^xy)(y)/ (e^xy)(x)+1

which means:

$\displaystyle \frac{dy}{dx}=1-(e^{xy})\frac{y}{e^{xy}}x+1\,.$

And the equation:

dy/dy = (e^-xy) - y/ (e^-xy) + x

which means:

$\displaystyle \frac{dy}{dx}=(e^{-xy})-\frac{y}{e^{xy}}+x\,.$

On the other hand:

dy/dy= (1-e^(xy)(y)) / ((e^(xy))(x)+1)

means:

$\displaystyle \frac{dy}{dx}=\frac{1-e^{xy}(y)}{e^{xy}(x)+1}\,.$