program class2

      double precision x,t,dt,f,exact

      open(unit=13,file="data.d")

      dt = 0.4
      x = 0

      do 10 t = 0, 12, dt
         exact = 1.0/2.0*exp(-t)+1.0/2.0*sin(t)-1.0/2.0*cos(t)
         write(13,*) t,x,exact
         f = sin(t)-x
         x = x + f*dt + 0.5*(x-sin(t)+cos(t))*dt**2
 10   continue

      exact = 1.0/2.0*exp(-t)+1.0/2.0*sin(t)-1.0/2.0*cos(t)
      write(13,*) t,x,exact

      stop
      end