Solving ODE

[fraud profile]

Hi,

I am using lsode to solve a simple ODE on Octave 2.1.72.
The ode is:
Solve: y''(t) + y(t) =0
such that: 
y(0)=3 & y(pi/2)=3

My code for this is:

-------- file f.m ---------
function xdot = f (x, t)
  xdot = zeros (2,1);

  xdot(1) =  x(2);
  xdot(2) =  -x(1);
endfunction
---- end of f.m -----

-------- file ode.m ---------
 l = linspace (0, pi/2, 20);

y_min=[3;3];
    psi = lsode( "f", y_min, l );
  
plot(l,psi(:,1));
---- end of ode.m -----

I am getting correct answer with this. But lsode requires y_min which is actually the value of x(1) and x(2) at t=0. I have the value of x(1) at t=0 and t=pi/2.(I got the value of x(2) at t=0 by solving this on Matlab and then solved this by adding y_min=[3;3]; here). How can I use the given boundary conditions so that I don't need the values of x(2) to solve the problem.

Thank you