I cannot provide you the piece of code I have written for computer-related problems
But what I did is sufficiently simple for me to give you a sketch of it

Step 1 :

EasySys := {diff(v(t), t)=0, diff(h(t), t)=w(t), siff(w(t), t)=0}  # if I am not mistaken
EasySol := dsolve ( EasySys, {v(t), h(t), w(t)})                       # which can be done manually

Step 2:

HarderSys := {diff(x1(t), t)=v(t)*cos(h(t)), diff(x2(t), t)=v(t)*sin(h(t))}
HarderSys := subs(EasySol, HarderSys):
HarderSol := dsolve(HarderSys, {x1(t), x2(t)})                        # easily found too

FullSol := EasySol union HarderSol;

I am not certain it is the solution you were searching for (no numerics here)
Probably someone will provide you a clever solution

Hope I helped

try  printf("%g\n",p) to add a carriage return and printf("%g\n\n",p) to skip a line after the print