I'm not sure on how to start this higher order diff eq. Solve $$1001y''' + 3.2y'' + \pi y' - \sqrt{4}y = 0$$
Initial Conditions:
$$y(0) = 0, y'(0) = 0, y''(0) = 0$$
I plugged it into the characteristic equation, but I don't know where to go from there...
$$1001r^3 + 3.2r^2 + \pi r - 2 = 0$$
Some help would be appreciated, thanks.

I think the point of this problem is that, by the uniqueness theorem, there is only one solution, and from the initial conditions, it is clear that $y(t)=0$ is that solution.  I don't think you were supposed to mess with the characteristic equation at all.  
