# Homework Help: Using reduction of order (conceptual) problems

1. Feb 20, 2012

### fufufu

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