Question

Write the initial value problem as a system of 1st order equations using vector notation:

y''+2y'+4y=3cos(2t), y(0)=1, y'(0)=0

Answer 1

r^2+2r+4=0
now?

Answer 2

so you would need to do two integrals in order to get the original equation. How comfortable are you in integration?

Answer 3

Perhaps put y' = x as the first equation and substitute accordingly for the second.