Here, the first using DifferentialEquations took 1 minute (with precompilation) and the second took 20s. I am using Julia 1.5.3 (in 1.6 I suppose that is faster).
So probably there is something broken in your installation, yes.
Edit: Unfortunatelly I was not able to install it on 1.6-rc1, the download gets stuck somewhere. I am not sure if this is a temporary problem on the server (edit: it is a bug fixed in 1.6-rc2, it seems). (on the nightly build the using takes 5 seconds here).