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February 13th, 2014, 05:02 AM   #1
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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
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February 13th, 2014, 06:18 AM   #2
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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".
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February 13th, 2014, 06:42 AM   #3
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Re: Elementary Differential Equation Problems

Oh My God I didn't Realize it was such a simple problem, Thank you so much
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February 13th, 2014, 01:56 PM   #4
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Re: Elementary Differential Equation Problems

Hello, joseph95!

These are elementary integration problems.,
[color=beige]. . [/color]Did you forget the basic formulas?


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