Variation of Parameters

  • Thread starter Cafka
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Hello,
I'm trying to understand this concept. Jere's the problem i'm doing.
I have to find the general solution for:
y'' + 36y = -4xsin(6x)

So you then solve for your characteristic equation and get lamda = +/- 6
so y1 = e^-6x and y2 = e^6x
You get your matrix for w, w1, and w2.
w = 12
w1 = 4xe^6xsin(6x)
w2 = -4xe^-6xsin(6x)

I have the problem at getting u1 and u2.
u1 = 1/3 the integral of xe^6xsin(6x) dx
u2 = -1/3 the integral of xe^-6xsin(6x) dx

How do you do that integration?

Thanks for your help,
Tom
 
17
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Your characteristic equation should be of the form y=Asin6x+Bcos6x since the the squareroot of -36 is 6i and -6i =)
 

dextercioby

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Yeah,and Lagrange's method kicks ass.So apply it.

Daniel.
 
193
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I was wondering if anyone knew of any good references on solving systems of equations involving trigonometric equations. Any information would be appreciated.
 
193
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Found the answer - I had forgotten Cramer's rule.
 

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