My Math Forum solution of differential equation

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 February 12th, 2016, 10:22 PM #1 Member   Joined: Nov 2012 Posts: 61 Thanks: 0 solution of differential equation Find solution of y" + 2y' + 5y =( 4cos2x)(e^-2) If y(0)=y'(0)=0 Thanks for help.plz show the method also
 February 12th, 2016, 10:52 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,696 Thanks: 2681 Math Focus: Mainly analysis and algebra Are you missing an $x$ in the exponential term? The characteristic equation yields $m = -1 \pm 2\mathrm i$ so for the method of undetermined coefficients we may try $y_p = (A\cos 2x + B\sin 2x)\mathrm e^{-2x}$ because none of those terms exist in the complementary solution.
 February 13th, 2016, 12:14 AM #3 Member   Joined: Nov 2012 Posts: 61 Thanks: 0 Yes, it is e^(-2x). Please tell the solution... it's urgent... Last edited by skipjack; February 15th, 2016 at 01:53 PM.
 February 14th, 2016, 08:33 AM #4 Senior Member   Joined: Dec 2015 From: Earth Posts: 823 Thanks: 113 Math Focus: Elementary Math $\displaystyle y=e^{-3x}[\frac{2}{5}e^{x}(2\sin2x+\cos2x)+c]$ Last edited by skipjack; February 15th, 2016 at 01:51 PM.
February 14th, 2016, 08:38 AM   #5
Math Team

Joined: Dec 2013
From: Colombia

Posts: 7,696
Thanks: 2681

Math Focus: Mainly analysis and algebra
Quote:
 Originally Posted by rakmo Please tell the solution... it's urgent...
Perhaps you should put some effort in. Show some of your work.

Last edited by skipjack; February 15th, 2016 at 01:54 PM.

 February 15th, 2016, 10:02 AM #6 Member   Joined: Nov 2012 Posts: 61 Thanks: 0 Thanks v8archie. You helped a lot. Because of you, I was able to figure it out and it helped me in exam. Last edited by skipjack; February 15th, 2016 at 01:54 PM.
 February 15th, 2016, 12:40 PM #7 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,696 Thanks: 2681 Math Focus: Mainly analysis and algebra No problem.
 February 15th, 2016, 01:50 PM #8 Global Moderator   Joined: Dec 2006 Posts: 21,105 Thanks: 2324 According to W|A, y = e^(-2x)(2(9e^x - 8)sin(2x) - 4(e^x - 1)cos(2x))/17.

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