function [out] = Ex1(x, y, flag)%%  Evaluate the right hand side function for the%  ODE%                         %    y_1'(x) =  y_2(x)%               %    y_2'(x) =  4*y_1(x) + 3*y_2(x) - 8*exp(x) * cos(2x)%                %%  This system is equivalent to the second order ODE%%    z''(x) - 3 z'(x) - 4 z(x) = - 8 exp(x) * cos(2x)%%  The exact solution of the system with initial conditions%%    y_1(0) =  2 + 10/13             %    y_2(0) =  3 + 14/13%%  is given by%    y_1(x) =  exp(-x) + exp(4*x) %               + 10/13 * exp(x) * cos(2x) + 2/13 * exp(x) * sin(2x)%               %    y_2(x) = -exp(-x) + 4 * exp(4*x) %               + 14/13 * exp(x) * cos(2x) - 18/13 * exp(x) * sin(2x)%switch( flag )   case '' % return right hand side       out  = [ y(2);                4*y(1) + 3*y(2) - 8*exp(x) .* cos(2*x) ];      case 'jacobian' % return Jaacobian of right hand side       out  = [ 0   1;                4   3 ];   otherwise       error (['Unknown request.'])end