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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 April 20th, 2015, 08:43 AM #1 Senior Member   Joined: Jan 2015 From: usa Posts: 104 Thanks: 1 diff equation hi can someone please help me solve this problem: a) determine all the functions y: ℝ → ℝ which satisfy y '' (x) -5y '(x) + 6y (x) = x, x ∈ ℝ b) determine all sequences (xn) n> = 0 which satisfy x{n+2}-5x{n+1} +6x{n} = n , n∈N here's what I've done: a) homogeneous solutions are of the form y (x) = + λe2x μe3x , λ, μ ∈ ℝ we look for a particular soulution of the form y (x) = a + bx Differentiating this solution and by using the diff equation we find y (x) = 1 / 6x + 5/36 so the general solution is y (x) = + λe2x μe3x + 1 / 6x + 5/36 but I can not answer the question b) can someone Please help.thanks in advance. April 20th, 2015, 09:47 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,689 Thanks: 2669 Math Focus: Mainly analysis and algebra The homogeneous solution is $A2^n + B3^n$ and you can try $a + bn$ for a particular solution. April 20th, 2015, 10:04 AM #3 Senior Member   Joined: Jan 2015 From: usa Posts: 104 Thanks: 1 equ diff hi thanks for your help can you please tell me how did you find that the homogenuous solution is A2^n + B3^n thanks April 20th, 2015, 10:13 AM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,689 Thanks: 2669 Math Focus: Mainly analysis and algebra I looked at your exponential terms for the differential equation! More seriously, the roots of the characteristic polynomial are the exponents in the solution to the differential equation and the exponential bases in the solution to the difference equation. Tags diff, equation 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 Hatmpatn Differential Equations 5 December 16th, 2014 08:12 AM Jhenrique Calculus 4 May 11th, 2014 04:54 AM gen_shao Calculus 3 July 9th, 2013 12:52 PM Niko Bellic Calculus 2 July 8th, 2013 10:01 AM zgonda Calculus 1 November 27th, 2010 04:23 PM

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