Understanding Non-Real Eigenvalues to Solving Homework Problems

[cowmoo32]

Homework Statement

The Attempt at a Solution

I know the general form should be

x₁(t)=-C₁sin(3t) + C₂cos(3t)
x₂(t)=C₁sin(3t) + C₂cos(3t)

but there's something going on with v that I'm not getting. I'm not sure how to incorporate it without knowing A

 

[Mark44]

Homework Statement

The Attempt at a Solution

I know the general form should be

x₁(t)=-C₁sin(3t) + C₂cos(3t)
x₂(t)=C₁sin(3t) + C₂cos(3t)

The constants shouldn't be the same in both functions.

but there's something going on with v that I'm not getting. I'm not sure how to incorporate it without knowing A

 

[cowmoo32]

Whoops, I wrote that wrong. All of the problems I have worked so far have had the form:x₁(t)=-C₁sin(3t) + C₁cos(3t)
x₂(t)=C₂sin(3t) + C₂cos(3t)

 

[cowmoo32]

After looking through some more examples, the answer will have the form


x₁(t)=-C₁sin(3t)*a + C₁cos(3t)*b
x₂(t)=C₂sin(3t)*a + C₂cos(3t)*b

where v=a+ib

v = [-1-i,1] = [-1,1]+i[-1,0]

a=[-1,1]
b=[-1,0]

I get:
C₁sin(3t)
-C₂cos(3t)

But it's telling me that's incorrect.