# Differential equation using complex exponentials

1. Sep 22, 2011

### Slimsta

1. The problem statement, all variables and given/known data
Find three independent solutions to the differential equation
$\frac{d^3}{dt^3}$f(t) + f(t) = 0
You should use complex exponentials to derive the solutions, but express the results in real
form.

2. Relevant equations

$sin\theta = \frac{e^{i\theta} - e^{-i\theta}}{2i}$
$cos\theta = \frac{e^{i\theta} + e^{-i\theta}}{2}$

3. The attempt at a solution
I copy notes in class, tried to read the chapter but I don't see anything that helps me get the question

2. Sep 22, 2011

### Slimsta

someone?

3. Sep 22, 2011

### Swalker

I would recommend trying a solution of the form f(t) = A sin (theta) + B cos (theta) where you can replace the sin and cos with the relevant equations.

Once you establish the function then differentiate and solve for your A and B.