function value = blowup_exact ( t )

%*****************************************************************************80
%
%% blowup_exact() evaluates the exact solution of the blowup ODE.
%
%  Discussion:
%
%    y' = y^2
%    dy/y^2 = dt                   (Separation of variables)
%    -1/y = t + C                  (Antiderivatives)
%     y = - 1 / ( t + C )
%     C = - t0 - 1/y0
%     y = - 1 / ( t - t0 - 1/y0 )  (Exact formula)
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    29 April 2021
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    real T(:): the evaluation times.
%
%  Output:
%
%    real Y(:): the exact solution values.
%
  [ t0, y0, tstop ] = blowup_parameters ( );

  if ( y0 == 0.0 )
    value = zeros ( size ( t ) );
  else
    value = - 1.0 ./ ( t - t0 - 1.0 / y0 );
  end

  return
end

