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 Calculus Calculus Math Forum

 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'' + (t-2)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) ln|X(s)| = -4ln|s + 1|+ lnC = ln|1/(s + 1)^4| + lnC = ln|C/(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...  Tags laplace, separate, variables Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post sarah1994 Algebra 2 October 29th, 2013 12:16 PM Deiota Calculus 1 April 28th, 2013 10:28 AM arslan894 Elementary Math 5 February 22nd, 2012 01:23 PM The Chaz Calculus 1 August 5th, 2011 09:03 PM gplush Algebra 1 August 25th, 2009 11:17 AM

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