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July 18th, 2013, 10:11 AM  #11 
Senior Member Joined: Sep 2012 Posts: 112 Thanks: 0  Re: 2 exact differential equation
Thank you so much Mark! My Q.1 has been solved too.

July 19th, 2013, 10:53 AM  #12 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: 2 exact differential equation
Another method, cleverly suggested here, is to begin with: Now, switching to polar coordinates, we then eventually get: Integrating, we obtain: Back substituting for and , we get: Using the identity: we see this is equivalent to the result I gave before. 
July 19th, 2013, 09:21 PM  #13 
Senior Member Joined: Sep 2012 Posts: 112 Thanks: 0  Re: 2 exact differential equation
Thank you so much! To me the earlier solution is easier. 

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