## Help with initial value problem(IVP)

Hello experts!

As we know that there are 3 different general solutions of an ordinary differential equation depends on that what type of roots we've gotten in the solution, listed below.
1) y(t)=c1em1t+c2em2t
2) y(t)=c1emt+c2temt
3) y(t)=c1eucos(v)+c2sin(v)

Now 1st solution is used when discriminant i.e. D>0, 2nd is used when D=0 and 3rd is used when D<0

But here is a question,
y''+6y'+9y=0
By solving we get roots,
m1=-3 and m2=-3
While discriminant is -30
& book has used 2nd solution to solve it, if D<0 it must use 3rd solution.

How do we choose correct solution? Does solution is according to nature of roots(discriminant) or m1 & m2?