February 21st, 2011, 11:06 PM  #1 
Member Joined: Jul 2010 Posts: 34 Thanks: 0  Separation of Variables
I'm trying to solve the following ODE  (2xy 5)dx + (x2 + y2 )dy = 0, initial conditions y(3) =1; but I can't even separate the variable successfully. My workings so far  (2xy 5)dx + (x^2 + y^2 )dy = 0 2xydx  5dx + x^2dy + y^2dy = 0 2xydx + x^2dy + y^2dy = 5dx 2xy + (x^2dy)/dx +( y^2dy)/dx = 5 2xy + X^2 y' + y^2 y' = 5 (SUBSTITUTING dy/dx for y') 2xy/y' + x^2 + y^2 = 5/y' Now, if I'm on the right track (which I suspect I'm not) I just need to separate the that first term  2xy/y'.. I think. Help. 
February 21st, 2011, 11:57 PM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 2  Re: Separation of Variables
It's exact. Integrating the dx part with respect to x, and the dy part with respect to y, you get x²y  5x + f(y) and x²y + y³/3 + g(x) respectively, so you have 
February 22nd, 2011, 02:06 PM  #3 
Member Joined: Jul 2010 Posts: 34 Thanks: 0  Re: Separation of Variables
I see. I was unaware of exact DEs. Thanks for the solution and the link.


Tags 
separation, variables 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
PDE Separation of Variables method  Sefrez  Applied Math  1  October 26th, 2013 09:21 AM 
Price Elasticity, Separation of Variables  John Creighton  Economics  0  March 16th, 2012 08:46 PM 
Separation of Variables  engininja  Calculus  4  September 22nd, 2010 11:58 PM 
separation axiom  blbl  Real Analysis  3  May 26th, 2010 07:03 AM 
Separation of Variables  zaserov  Calculus  1  October 25th, 2007 01:11 PM 