Reduction of order from 2nd to 1st

[Kirstyy]

I have been given the equation:
y'' + y' - 2y = 0
and asked:
" Express the equation as a 1st-order system. Solve the system using matrix methods."

I thought in order to reduce an equation you needed one solution to it already. I tried using the general solution but it got messy.

Someone please help?

 

[D H]

Hint #1: Make the substitution y'=z. This should give you a first order ODE involving two variables (as opposed to a second order system of one variable).

Hint #2: Express this first order system in matrix form.

Hint #3: This is almost certainly in your text and in your lecture notes.