program hw5number6

c     Program using Euler's method to determine an approximate
c     solution to problem 7.9-3 in Boyce and DiPrima, 8th edition.
c
c     The initial conditions are (x1,x2) = (4,0).
c
c     To compile on a linux machine type
c
c     "g77 7.9-3.c -lm"
c
c     and then to execute it, type "a.out".
c
c     The data file is called "data.d".
     
      double precision x(2),derivs(2),t,dt,tf
      double precision exact(2)

      dt = 0.001
      tf = 50.0
      x(1) = 4.0
      x(2) = 0.0
      

      open(u,FILE='data.d',STATUS='OLD')
      do 10 t=0.0,tf,dt
         exact(1) = 7.0*cos(t) + 4.0*sin(t) + 2.0*t*cos(t)-t*sin(t) 
     c        - 3.0*cos(t) + sin(t)
         exact(2) = 2.0*cos(t) + 3.0*sin(t) + t*cos(t) - 2.0*cos(t)
         
         write(u,*) t,x(1),x(2),exact(1),exact(2)
         
         derivs(1) = 2.0*x(1) - 5.0*x(2) - cos(t)
         derivs(2) = x(1)- 2.0*x(2) + sin(t)

         x(1) = x(1) + derivs(1)*dt
         x(2) = x(2) + derivs(2)*dt
 10   continue
      stop
      end