Differential equation using complex exponentials

[Slimsta]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

I'm not entirely sure what to do.. please help
I copy notes in class, tried to read the chapter but I don't see anything that helps me get the question

 

[Slimsta]

someone?

 

[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.