Separable Equations DFQ #2

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January 19th 2009, 10:58 AM
cheertcc101

Separable Equations DFQ #2

Ok so I really do think that this one is a separable equation but if not maybe someone could let me know that too haha

I need to separate this equation to have the dy and y's on one side and and the dx and x's on the other so I can integrate and solve the problem.

[(y*e^(xy))-(1/y)]dx + [(x*e^(y))+(x/(y^2))]dy=0

I have no idea how to separate the equation!

Any hints or first steps would be nice!!! THANK YOU!!!!
January 19th 2009, 11:11 AM
Danny

Quote:

Originally Posted by cheertcc101

Ok so I really do think that this one is a separable equation but if not maybe someone could let me know that too haha

I need to separate this equation to have the dy and y's on one side and and the dx and x's on the other so I can integrate and solve the problem.

[(y*e^(xy))-(1/y)]dx + [(x*e^(y))+(x/(y^2))]dy=0

I have no idea how to separate the equation!

Any hints or first steps would be nice!!! THANK YOU!!!!

It's not separable, the term $e^{xy}$ stops this. It is however exact meaning the is an $F$ such that

$dF = F_x \,dx + F_y,dy = \left( y e^{xy} - \frac{1}{y}\right) dx +\left( x e^{ x y} + \frac{x}{y^2} \right) dy = 0$

(I'm guessing a typo - the $e^{y}$ should be $e^{x y}$ in the second term).
January 19th 2009, 07:26 PM
cheertcc101

Alright so i agree that it would make way more sense for there to be a typo in the second part of the equation and if there is then I know how to do the problem BUT the teacher didnt say anything about a typo SOO i was wondering if for some reason there was NOT a typo then is there a way to still work the problem. I looked for special integration factors but found nothing .. maybe Im missing something or if there is no way to work the problem without a typo then I would like to know that too.

THANKS for the help thus far!