2nd order homogeneous equations complex root

[Larrytsai]

Homework Statement

y'' -2y' +5y =0 , y(0)=1, y'(0)=1
you get a complex root conjugate.

Homework Equations

y=e^(rt)
y'=re^(rt)
y''=r^2 * e^(rt)

The Attempt at a Solution

I have in my notes sin(omega*t)e^(sigma *t), cos(omega *t)e^(sigma).
I don't think i took down the notes properly, can anyone care confirm if this is right or wrong?

 

[rock.freak667]

Yes your homogeneous solutions are sin(ωt)e^σt and cos(ωt)e^σt when the roots are in the form r=σ ± ωi with 'i' being the imaginary unit.