function euler( F, tspan, y0, n )

#*****************************************************************************80
#
## euler() uses Euler's method to integrate a simple ODE.
#
#  Discussion:
#
#    The exact solution is:
#
#      y(t)=(7.1+(3//10)*sin(t)*exp(3t)-
#        (1//10)*cos(t)*exp(3t))*exp(-3t)
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    09 March 2024
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    function F(t,y):
#
#    real tspan[2]:
#
#    real y0:
#
#    integer n:
#
#  Output:
#
#    real t[n+1], y[n+1]:
#
  dt = ( tspan[2] - tspan[1] ) / n

  t = zeros(n+1)
  y = zeros(n+1)

  t[1] = tspan[1]
  y[1] = y0
  for i in 1 : n
    t[i + 1] = t[i] + dt
    y[i + 1] = y[i] + dt * F( t[i], y[i] )
  end

  return t, y
end