Trajectories of a non linear control system

How can i plot the trajectories of x^2+y^2=c where c can be 1,2,3 etc

[Verisign]

The system is dx1=x2, dx2=-1.5*x1

Answer 1

[Torsten]

Solution is

x1(t)=a*sin(sqrt(1.5)*t)+b*cos(sqrt(1.5)*t)
x2(t)=sqrt(1.5)*[a*cos(sqrt(1.5)*t)-b*sin(sqrt(1.5)*t)]

And now ?

Best wishes

Torsten.