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May 4th, 2016, 08:42 AM  #1 
Newbie Joined: May 2016 From: india Posts: 3 Thanks: 0  ordinary diff. eq.
solve the differential equation : dydx = 2xydy 
May 4th, 2016, 09:14 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,689 Thanks: 2669 Math Focus: Mainly analysis and algebra 
What happens if you write $v=xy$?

May 4th, 2016, 09:22 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 21,019 Thanks: 2254 
Use $e^{\text{y}^2}\!\!$ as an integrating factor.

May 4th, 2016, 09:56 AM  #4 
Newbie Joined: May 2016 From: india Posts: 3 Thanks: 0  
May 4th, 2016, 03:10 PM  #5 
Senior Member Joined: Dec 2015 From: somewhere Posts: 712 Thanks: 96 
Solution can be approximated there is no exact solution as i can see 
May 4th, 2016, 05:06 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,019 Thanks: 2254 
Given $dy = 2xydy + dx$, multiplying by $e^{y^2}\!\!$ gives $e^{y^2}dy = 2xye^{y^2}dy + e^{y^2}dx = d\!\left(\!xe^{y^2}\!\right)\!$, etc.


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