program oct1416

      real x(2),t,dt,tfinish,xe,f1,f2
      integer i,steps 

      x(1)=1
      x(2)=-1
      dt = 0.01
      tfinish=20
      steps=tfinish/dt
      open(unit=13,file="data.d")
      
      do 10 i=1,steps
         xe=51.0/47.0*cos(sqrt(3.0/2.0)*t)-sqrt(2.0/3.0)*
     c        sin(sqrt(3.0/2.0)*t)-4.0/47.0*cos(5.0*t)
         write(13,*) t,x(1),x(2),xe
         x(1)=x(1)+f1(x,t)*dt
         x(2)=x(2)+f2(x,t)*dt
         t=t+dt
 10   continue
      xe=51.0/47.0*cos(sqrt(3.0/2.0)*t)-sqrt(2.0/3.0)*
     c     sin(sqrt(3.0/2.0)*t)-4.0/47.0*cos(5.0*t)
      write(13,*) t,x(1),x(2),xe

      close(13)

      stop
      end

      real function f1(x,t)
      real x(2),t
      f1 = x(2)
      return 
      end

      real function f2(x,t)
      real x(2),t
      f2=0.5*(4.0*cos(5.0*t)-3.0*x(1))
      return 
      end