Matrix Differential Equation with Generalized Eigenvectors

patchwerk

Hey guys, need some quick help before an exam

I have a differential eqn.

x' = | 0 1 | *x , and initial conditions x(0) = |2|
| -25 10 | |3|

I find that there are two eigenvalues 5, and 5

The corresponding eigenvector to 5 is [1 5] (vertical)

So i need to find a generalized eigenvector,

I do so in the form

(A - 5lambda)v_2 = v_1

I then find that v_2 = [0 1 ] (vertically)

I don't know what form my solution should now be in

Please help, I have an exam at 7,

Thanks,

Evan

patchwerk

the matrix is R1: 0 1 and R2: -25 10
and the IC is x(0) = R1:2 R2:13

sorry, not sure hwo to enter matrices

patchwerk

R2: is 3 sorry!