I have used Euler's method before but it was based on a program. As for deriving Euler's I am unsure of that. I don't think it would be tayler expansion solely because we learned that after I received an assignment with this question.
Ok so for this problem I have to use IVPs to prove that cos^2(x)+sin^2(x)=1. I know the end result is suppose to be:
du/dt= - v, u(0)=1
dr/dt= u, v(0)=0
but I have no idea how to go about getting to this point.