December 2nd, 2010, 04:55 AM  #1 
Member Joined: Sep 2010 Posts: 73 Thanks: 0  laplace  separate variables
I'm supposed to find a nontrivial solution to tx'' + (t2)x' + x = 0, x(0) = 0. You don't really need to know that but just in case. I got to this point: (s+1)X'(s) + 4X(s) = 0 Now I need to separate variables to find a solution but I've been working on this for two days and can't figure out how to get to the correct solution, which is: X(s) = C/(s+1)^4 So my question is, how do I go from the first equation to the second using separation of variables? Thanks! 
December 2nd, 2010, 09:03 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: laplace  separate variables
(s+1)X'(s) + 4X(s) = 0 (s+1)X'(s) = 4X(s) X'(s)/X(s) = 4/(s + 1) lnX(s) = 4lns + 1+ lnC = ln1/(s + 1)^4 + lnC = lnC/(s + 1)^4 X(s) = C/(s + 1)^4 This is the second technique (after plain'ole integration!) in all of the diff EQ books that I have... 

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