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Using reduction of order (conceptual) problems

  1. Feb 20, 2012 #1
    1. The problem statement, all variables and given/known data
    I have a nonhomogeneous 2nd order DE and im given one solution to it and told to use variation of parameters?
    to get the general solution. First i need to get the 2nd solution though. Should I use reduction of order to get the 2nd solution? If so, then in what form should the equation be in before i start using reduction of order? The complementary solution is the solution to a homogeneous equation right? So should g(t) = 0 before using reduction of order?
    heres what I mean..
    the equation is:

    (t-1)^2(y'') - 4(t-1)y' + 6y = t

    so in order to use reduction of order should i write the equation as:
    (t-1)^2(y'') - 4(t-1)y' + 6y = 0

    and then proceed?

    also, do i first need to divide through with the coefficient of y'' or does that matter?

    Sorry if im explaining this sort of retardedlike but im struggling with it..
    pleas help...thanks!

    ( fyi, the given solution is y_1 = (t-1)^2 )

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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