changing the ode inside ode45

Hi everyone, I'm trying to solve an ode using ode45 which comes basically from matrix second order ode.

My idea is to solve first for dudx(2)=(sin(x)-z)*u(1) then solve for dudx(2)=(cos(x)-z)*u(1) as well as

adding the new solution to the first one to build a matrix of these two solutions.

I've tried this but because I have a function with a variable x so it doesnt work as a parameter

inside the function hundle.

Any idea would be appreciated and here is my code:

clear all
z=-1;
N=10;
xspan = [0 2*pi];
u01 = [1 0]; 
u02 = [0 1];
opts = odeset('RelTol',1e-9,'AbsTol',1e-9);
[u1] = ode45(@(x,u) ode(x,u,z),xspan,u01,opts);
[u2] = ode45(@(x,u) ode(x,u,z),xspan,u02,opts);
x1 = linspace(0,2*pi,N);
y1 = deval(u1,x1);
y2 = deval(u2,x1);
y1 = y1(:,end);
y2 = y2(:,end);
Phi = [y1 , y2];
 
    
    
       
function dudx = ode(x,u,z)
dudx = zeros(2,1);
dudx(1) = u(2);
dudx(2) = (sin(x)-z)*u(1);
end