Hey Levis. Im a dane too, and i am currently on my first year of a bachelors degree in physics. I just took my exam in Linear Algebra today (i noticed your remark on how simple vector operations are :) ) and i feel that i can safely tell you, that if you are already this proficient with mathematics (just the fact that you know enough calculus to be constructing differential equations) and if you continue to challenge yourself like this until you reach your first year of university, you are going to have a pretty easy time here.
by the way, im studying at KU. What gymnasium are you at?