# A ode question

1. Jul 10, 2010

### tennishaha

1. The problem statement, all variables and given/known data

y''+y'+y=0

2. Relevant equations

say we get the roots: -1/2+i*sqrt(3)/2 and -1/2-i*sqrt(3)/2

3. The attempt at a solution
I saw two solutions to this problem
first is
y=e^(-1/2*x)(c1*cos(sqrt(3)/2*x)+c2*sin(sqrt(3)/2*x))
second is
y=c1*e^[(-1/2+i*sqrt(3)/2)*x]+c2*e^[(-1/2-i*sqrt(3)/2)*x]

which one is correct? I think the two solutions are different
thanks

2. Jul 10, 2010

Euler's Formula states:

$$e^{i\theta} = \cos(\theta) + i\sin(\theta).$$

Can you fill in the remaining steps? I hope this helps.

3. Jul 11, 2010

### HallsofIvy

Staff Emeritus
Using Euler's formula, as Raskolnikov suggests, you should find that the two functions are the same. (Possibly different constants, of course.)