program class4

      double precision x,t,dt,f,exact,k1,k2,k3,k4

      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

         k1 = f(x,t)*dt
         k2 = f(x+0.5*k1,t+0.5*dt)*dt
         k3 = f(x+0.5*k2,t+0.5*dt)*dt
         k4 = f(x+k3,t+dt)*dt

         x = x + (k1+2*k2+2*k3+k4)/6.0

 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

      double precision function f(x,t)
      double precision x,t

      f = -x + sin(t)

      return
      end