function y = sensitive_exact ( t )

%*****************************************************************************80
%
%% sensitive_exact() evaluates the exact solution of sensitive_ode().
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    03 December 2021
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    John D Cook,
%    Sensitive dependence on initial conditions in ODE's,
%    12 November 2013,
%    https://www.johndcook.com/blog/2013/11/12/sensitive-dependence-on-initial-conditions/
%
%  Input:
%
%    real T(:): the times.
%
%  Output:
%
%    real Y(:,2), the exact solution values.
%
  [ t0, y0, tstop ] = sensitive_parameters ( );

  ep = y0(1) - 1.0;

  n = size ( t, 1 );
  y = zeros ( n, 2 );
  for i = 1 : n
    y(i,1) = ( 1.0 - ep / 2.0 ) * exp ( - t(i) )...
           +         ep / 2.0   * exp ( t(i) );
    y(i,2) = - ( 1.0 - ep / 2.0 ) * exp ( - t(i) )...
             +         ep / 2.0   * exp ( t(i) );
  end

  return
end
