
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 2nd, 2015, 05:57 PM  #1 
Newbie Joined: Sep 2014 From: n/a Posts: 9 Thanks: 0  Using Separation of variables
Hello everyone, I am having an issue with this concept. I am running into having a second order differential equation when I am using the separation of variables method. I would normally type the problem into this text space but I figured it was better for me to upload a picture created from microsoft's word processor with the formatting of equations. Please see attached jpeg for problem. So since I have a second order and there are three different ways for me to solve a second order, would the general solution of the second order include a summation to cover for all three cases? Last edited by philm; May 2nd, 2015 at 06:00 PM. Reason: Forgot to upload document 
May 2nd, 2015, 08:51 PM  #2 
Senior Member Joined: Aug 2014 From: United States Posts: 136 Thanks: 21 Math Focus: Learning 
Yes, I believe that the general solution is the sum of all distinct solutions. Assuming all different methods give you different solutions, your answer would be a sum of all those solutions.

May 3rd, 2015, 03:48 PM  #3 
Newbie Joined: Sep 2014 From: n/a Posts: 9 Thanks: 0 
Hm, intersting, There are three different cases depending on the complex roots of the 2nd order characteristic equation. This is all good and everything but the lambda is causing a huge issue since it is unknown. After working out the complex roots, I determined the three cases (w = lambda) 1) w = 1/4 2) w > 1/4 3) w < 1/4 I am not too sure but I think that there is a particular case that I have to choose from for this specific problem? Or do I have to solve the PDE for all three cases? 
May 5th, 2015, 03:38 PM  #4 
Newbie Joined: Sep 2014 From: n/a Posts: 9 Thanks: 0 
I was able to solve this problem

May 6th, 2015, 05:37 AM  #5 
Senior Member Joined: Aug 2014 From: United States Posts: 136 Thanks: 21 Math Focus: Learning  
May 6th, 2015, 10:41 AM  #6 
Newbie Joined: Sep 2014 From: n/a Posts: 9 Thanks: 0 
I had to take the summation of the separation of variables. Then, u(x, t) only existed at one value, n = 1. At that point, lambda went away. It was a little tricky this one. Then I solved the 2nd order ODE using IC and BC. 

Tags 
separation, seperation, 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  2  February 22nd, 2011 01:06 PM 
Separation of Variables  engininja  Calculus  4  September 22nd, 2010 11:58 PM 
Separation of Variables  zaserov  Calculus  1  October 25th, 2007 01:11 PM 