Solving Differential equations involving Trigonometric functions.

Questions
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1

Hey all,

I have a differential equation in polar coordinates which descrive time rate of change of r and \theta.
The equation involves Sin and Cos, following is what I write in Mathematica.

traj= Assuming[ y[t] > 0 &&  y[t] < 2*Pi, {DSolve[{x'[t] == n Cos[y[t]], y'[t] == (1/x[t]) (1 - n Sin[y[t]]), x[0] == x10, 
     y[0] == 0}, {x[t], y[t]}, t]}]

You can see the equations are fairly simple. However, Mathematica cribs about inverse functions and being used and gives the solution which is not useful.

Can anyone here provide some help?

2

Looking through the solution I get in Mma7(Win-64), I see that you may need to:
(1) specificy some initial or boundary condition to eliminate the C[1].
(2) Plot your solution (or even generate a table of values) by
(a) Specify values for x10, n etc and then
(b) use the techniques in “Neat Examples” available at the following URL, to plot (or table the answer).

My apologies for not trying with dummy values, beacuse i’m not familiar with the equation and it’s easy to go on a wild goose chase if the proper initialization is not provided.