Tried to show the emperical order of the 3 methods with no drag, but only euler gave me its correct order (1). Heun and RK4 were identical as expected in a vacuum, they had order of 0.93. I researched the reaosn why it was not 2, and found that the landing-point linear interpolation error was the cause of it.
In the graph you can see how the error decreases with lower dt, and increases as dt increases. Expected.