# Three coupled trig differential equations

Not able to Reduce coupled equations with Inverse functions of three variables and a constant. Please help.

  uvw = {u'[t] == Sin[v[t]]/rh - Sin[v[t]] Sin[u[t]]/w[t],
v'[t] == Cos[v[t]] Cos[u[t]]/w[t] Tan[u[t]]^2,
w'[t] == Sin[v[t]] Cos[u[t]]};
DSolve[uvw, {u, v, w}, t]

Clear[".*"]
rh=0.5;tmax=2.333
NDSolve[{u^\[Prime](t)\[LongEqual]sin(v(t))/rh-(0 *sin(u(t)) sin(v(t)))/w(t),v^\[Prime](t)\[LongEqual](cos(u(t)) tan^2(u(t)) cos(v(t)))/w(t),w^\[Prime](t)\[LongEqual]cos(u(t)) sin(v(t)),u(0)\[LongEqual]1.65,v(0)\[LongEqual]0.6,w(0)\[LongEqual]0.125},{u,v,w},{t,0,tmax}]
{u1_p,v1_p,w1_p}={u(p),v(p),w(p)}/. First[%]
Plot[{u1(t),v1(t),w1(t)},{t,0,tmax}]

• Are you sure there is an exact solution to this system? If no then try NDSolve? – zhk Oct 15 '17 at 12:45
• Simplified the first part thought to improve chances of solution and used NDSolve, but still the system is unresponsive. – Narasimham Oct 15 '17 at 14:00
• Your DSolve operator is written correctly, while the NDSolve and Plot ones are not. It is for this reason they do not work. The construct u^\[Prime] (t)` is illegal in Mma, The round brackets are not used with functions. After correcting these errors the system can be numerically solved, but its solution diverges. – Alexei Boulbitch Oct 15 '17 at 15:14