Systems of ODE's double-zero eigenvalues

[gabriels-horn]

Homework Statement

I put a triangle around the problem of interest.

Homework Equations

The Attempt at a Solution

I solved for the eigenvalues, resulting in double-zero values. My question is, using the variation of parameters method, which is what (14) refers to in the question. How do I solve for the second zero. For the first I get the matrix

([1]) *c1 for the general solution.
([1])

Do I need to add a guess such as t to the next zero eigenvalue?

 

[lanedance]

yeah so as you say, a constant value is your 1st general solution, i would try multplying by t and whether you can find a 2nd...

note also, that the column vectors of the matrix are the linearly dependent, and that x1' = x2' for all t