changing the ode inside ode45

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Haya M
Haya M 2020-11-16
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

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