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 June 4th, 2017, 10:13 AM #1 Newbie   Joined: Jun 2017 From: Romania Posts: 1 Thanks: 0 Math Focus: All of it General solutions for non-homogeneous diff eq Hey guys ! I have some troubles with these types of differential equations. I have to find the general solution of this eq : y''-4y'+5y=e^(2s) I have found the general solution of the homogeneous part of this eq. Yh= e^(2s) * ( c1* cos s - c2 * sin s ) I hope it's correct. Well, my problem comes at the particular solution. I don't understand how to find it. Can anyone help me? Thank you ! June 4th, 2017, 12:11 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Yes, that is the correct solution to the "associated homogeneous equation". I presume you know that the general solution to the entire equation is that general solution to the associated homogeneous equation plus a single solution to the entire equation. One method for finding that one solution, called "undetermined coefficients" is to look for a solution of the form $\displaystyle Pe^{2s}$ (we need to "determine" the coefficient P). If $\displaystyle y= Pe^{2s}$ then $\displaystyle y'= 2Pe^{2s}$ and $\displaystyle y''= 4Pe^{2s}$ so that $\displaystyle y''- 4y'+ 5y= 4Pe^{2s}- 4Pe^{2s}+ 5Pe^{2s}= 5Pe^{2s}= e^{2s}$ so that P= 1/5. The general solution to the differential equation is $\displaystyle y(s)= e^{2s}(A cos(s)+ B sin(s))+ (1/5)e^{2s}$. Thanks from romsek Last edited by skipjack; June 4th, 2017 at 11:28 PM. June 4th, 2017, 11:25 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 You slipped up; $P = 1$. Tags diff, general, nonhomogeneous, solutions 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 JustSomeGuy Calculus 4 January 26th, 2016 08:47 PM Hatmpatn Differential Equations 5 December 16th, 2014 08:12 AM Jhenrique Calculus 4 May 11th, 2014 04:54 AM IsaacAltair Calculus 1 July 1st, 2013 07:03 AM chris99191 Algebra 10 April 22nd, 2011 02:10 AM

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