% We are trying to find A that satisfies y(1) = 2
tspan = [0:.1:1];
alpha = -1;
beta = 2;
A = 1;
y0 = [alpha A];

options = odeset('AbsTol',10^(-6));

% A has to be greater than alpha, so A > -1.
% Begining with A = 1 we can move the value
% of A to the right or to the left using bisection
dA = 4;
tol = 10^(-6);
for j=1:1000 % Begin convergence loop 
  [t,y] = ode45('f',tspan,y0,options);
  if (abs(y(end,1)-beta) < tol) % check for convergence 
    break % get out of convergence loop 
  end 
  if (y(end,1) > beta) % this IF statement block checks to see if A needs to be higher or lower
    A=A-dA 
  else  
    dA=dA/2;     
    A=A+dA   
  end % 
  y0 = [alpha A]; % Update initial conditions
end % End convergence loop 

figure(1), plot(t,y(:,1),'g*-',tspan(1),alpha,'bs',tspan(end),beta, 'bo') % plot solution y 
set(gca,'FontSize',20)


%Alternatively use bvp4c