a) Equilibrium Solutions
> EQUILeqns := { rhs( ode1 ) = 0, rhs( ode2 ) = 0 } ;
> EQUILsoln := solve( EQUILeqns, VAR ) ;
The Maple output is a little messy. The equilibrium solutions are (easily) seen to be the origin (0,0) and the unit circle ( ).
>