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Differential Equations - Variation of Parameters problem

  1. Oct 30, 2008 #1
    As the name suggest, this problem is an undetermined coefficients problems where variation of parameters is necessary to solve. As with my previous question; This is not a homework problem, but it is out of the text book so I figured this would be the appropriate place to ask if I am doing it correctly.

    Here is the initial problem where one is asked to find the general solution;
    [​IMG]

    I know there are at least 4 different approaches to this problem, but nearly all will not work well on other similar problems. However, from what I can understand the "Variation of Parameters" technique can be used to solve almost any differential Equation problem in this format so long as you do not encounter an impossible-to-solve integral EXA:{ln(ln(x))}

    That being said; here is my attempt at the problem using "Variation of Parameters";
    [​IMG]


    Simple question; Did I do it right? If not where did I screw up?
     
  2. jcsd
  3. Oct 31, 2008 #2

    HallsofIvy

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    No, "undetermined coefficients" and "variation of parameters" are two completely different methods of find a specific solution to a non-homogeneous linear equation.

    In your equation for v'2 you seem to have neglected a factor of cos(x) on the right. You have cos2(x) from the differential equation. To solve for v2' you have to multiply by another cos(x). You should have v2'= cos3(x).
     
  4. Oct 31, 2008 #3
    Whoops... I should have caught that that problem with V2. Anyway thanks for the help, gotta remember to keep a close eye on everything in these problems... its pretty easy to loose track of parts of the problem since there are so many parts.
     
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