Differential equations, variation of parameters

[missavvy]

Homework Statement

Using variation of parameters, find the general solutions of the differential equation

Homework Equations

y''' - 3''y + 3y' - y = e^t / t
where e^t/t = g(t)

The Attempt at a Solution

I know how to solve these types of equations when its a second order, but I don't understand what to do for the particular solution since there are 3 solutions to the associated homogeneous equation, y1 = e^t, y2 = te^t, y3 = t²e^t.
Usually I would just take the 2 solutions and compute the Wronskian, then use the formula where it's -y1*integral([y2*g(t)]/W)dt + y2*integral([y1*g(t)]/W)dt.
Since there are three solutions though, I don't understand how to solve it. My textbook uses a different method where they use something like v1'y1 + v2'y2 + v3'y3 = 0, v1'y1' + v2'y2' + v3'y3' = 0, and then the next equation is the same except the y's are the 2nd derivatives and it = g(t).
Then they solve for v1, v2 and v3, integrate, and plug them into the homogeneous equation to get the particular solution.
Sorry if this isn't clear!

 

[broodfusion]

for Nth degree differential equation, there is a different formula.

http://img256.imageshack.us/img256/8756/dif2.jpg

Here, W(t) = W (y1,y2,y3,...,yn)(t)

and Wm(t) is the determinant obtained from W by replacing the mth column by the column (0,0,...,0,1)