July 18th, 2015, 12:58 PM  #1 
Senior Member Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4  Differential Equation Problem 2
Can someone help me spot what I'm doing wrong? Problem: $\displaystyle z=xy $ $\displaystyle \frac{dy}{dx} = \frac{xy+3}{xy3} $ My attempt: $\displaystyle \frac{dz}{dx} = 1 \frac{dy}{dx} $ $\displaystyle \frac{dy}{dx} =1  \frac{dz}{dx} $ $\displaystyle 1  \frac{dz}{dx} = \frac{z+3}{z3} $ $\displaystyle  \frac{dz}{dx} = \frac{z+3}{z3} 1 $ $\displaystyle  \frac{dz}{dx} = \frac{6}{z3} $ $\displaystyle \frac{z3}{6} * dz = dx $ After Integrating, $\displaystyle  \frac{z^2}{12} + \frac{3z}{6} = x+A $ $\displaystyle  \frac{(xy)^2}{12} + \frac{3x}{6} + \frac{3y}{6} $ Last edited by skipjack; July 18th, 2015 at 08:13 PM. 
July 18th, 2015, 02:11 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,377 Thanks: 2474 Math Focus: Mainly analysis and algebra 
You are missing the righthand side of the final line.
Last edited by skipjack; July 18th, 2015 at 08:13 PM. 
July 18th, 2015, 02:49 PM  #3 
Senior Member Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4 
Oh right, sorry, that would be $\displaystyle = x + C $ but my final answer doesn't match with the book I am using. :P Last edited by skipjack; July 18th, 2015 at 08:14 PM. 
July 18th, 2015, 04:19 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,377 Thanks: 2474 Math Focus: Mainly analysis and algebra 
Subtract $x$ from both sides? What answer are you looking for?
Last edited by skipjack; July 18th, 2015 at 08:11 PM. 
July 18th, 2015, 08:20 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,519 Thanks: 1746  
July 19th, 2015, 03:29 AM  #6 
Senior Member Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4 
The answer on the book is: $\displaystyle \frac{(xy)²}{2}+ 3x + 3y = C $ 
July 19th, 2015, 08:45 AM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,887 Thanks: 765 Math Focus: Wibbly wobbly timeywimey stuff.  

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