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February 13th, 2014, 05:02 AM  #1 
Newbie Joined: Feb 2014 Posts: 2 Thanks: 0  Elementary Differential Equation Problems
Hello everyone, this is my first post, English is not my mother tongue, so i'm sorry if there's some wrong / unclear statement.. I was doing some exercise, the problem was y'' + 9y = 9 ( sec 3t )^2 ; 0 < t < pi/6 so the homogeneous solution would be = C1*cos 3t + C2*sin 3t and using Variation of Parameters i end up with the particular solution u1 = u2 = I don't know how to solve those integration or maybe the particular solution above was wrong cus of miscalculation please reply ASAP cus next week is my first exam 
February 13th, 2014, 06:18 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Elementary Differential Equation Problems
I presume you know that and so your integrals are and . Since the first has cos(t) to an odd power and the second has sin(t) to an odd power, there is a standard method of integration that you probably learned in Calculus. In the second you can immediately let u= cos(t) so that du= sin(t)dt and the integral becomes . For the first, first multiply both numerator and denominator by cos(t) to get . Now let u= sin(t) so that du= cos(t)dt and the integral becomes which can be done by "partial fractions". 
February 13th, 2014, 06:42 AM  #3 
Newbie Joined: Feb 2014 Posts: 2 Thanks: 0  Re: Elementary Differential Equation Problems
Oh My God I didn't Realize it was such a simple problem, Thank you so much 
February 13th, 2014, 01:56 PM  #4  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Elementary Differential Equation Problems Hello, joseph95! These are elementary integration problems., [color=beige]. . [/color]Did you forget the basic formulas? Quote: Quote:  

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