function y = logistic_solution ( t, t0, y0 )

%*****************************************************************************80
%
%% logistic_solution returns the exact solution for the logistic ODE.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    07 February 2020
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    real T: the current time.
%
%    real T0, Y0: the initial time, and initial value.
%
%  Output:
%
%    real Y: the value of the solution to the logistic ODE.
%    
  y = 1.0 ./ ( 1.0 + ( 1.0 / y0 - 1.0 ) * exp ( t0 - t ) );

  return
end

