SCREEN 12
VIEW (90, 50)-(638, 328), 8, 4
WINDOW (-.5, 0)-(10.5, 40)
PRINT "Now the exact solution is calculated, at the computed points, that is."
PRINT "The points are accurate even for a large steplength: try .001 and 4."

x0 = 0: u = 10                                'Note that h has become x

PRINT "Initial level ="; x0; "Input U ="; u: PRINT
LINE (0, 0)-(10, 0), 9                        'Draw axis, blue
k = .5

DO
   INPUT "Step "; dt: IF dt = 0 THEN END
  
   g = EXP(-k * dt)            'Coefficients for exact solution
   h = (1 - g) / k
  
   x = x0                            'Initial values to x and t
   t = 0
   PSET (0, x0)                      'Move to starting point
   DO
      x = g * x + h * u              'This is the simulation
      t = t + dt
      LINE -(t, x)                   'This displays the result as lines
                                     'which join the computed points
   LOOP UNTIL t > 10
LOOP