Diff Eq: Variation of Parameters for 3rd-ODE's

UziStuNNa
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Homework Statement



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I don't see any attempt to do anything yourself.
 
Well I'm not sure how to start it off.
 
UziStuNNa said:
Well I'm not sure how to start it off.

Then you need to tell us what is confusing you.
 
W_1(t)= g(t)(y_2(t)y_3'(t)-y_3(t)y_2'(t))
W_2(t)=-g(t)(y_1y_3'-y_3y_1')
W_3(t)=g(t)(y_1y_2'-y_2y_1')

Then, u_1(t)=\int(W_1/W) and so forth for u_2[\tex] and u_3
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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