ode45 array issues

Running into issues with the familiar "Index exceedes array bounds" while using ode45.

Trying to figure out the value for k in the above code based on a system below and the dataset 'Data.MAT' consisting of 24 concentration and time measurements.

Can't figure out what's going on, I've tried defining my equation in a separate function (gave up on that) and instead followed the example on this Mathworks ode 45 example. I've used the same method before but can't understand why it's not working this time.

clc
clear all
close all

%% Loading and viewing data
Data = load('ProbData_hw3.MAT');
tspan = Data.time;
Ca_data = Data.Soln;

plot(tspan,Ca_data,'ko ')
xlabel('time')
ylabel('Measurement')

%% Setting up 

y0 = Ca_data(1);
learn_rate = .001;


k_started = [1 1.001];

%get things going to get dJ/dk
% Get J1
k = k_started(1);
b=sqrt(1.2*9.81*k);

syms y(t)
[V] = odeToVectorField(diff(y,2) == (-k/1)*(9.81/k +b*y) - diff(y));
f = matlabFunction(V,'vars', {'t','Y'});
[t, y] = ode45(f, [0 5], y0);

y_hat = interp1(t,y,tspan);
for n = 1:24
    tmp(n) =  (y_hat(n)-Ca_data(n))^2;
end
J1 = 1/n*sum(tmp);


for i = 1:500
    if i == 1
        k = k_started(2);
        Jold = J1;
        k_old = k_started(1);
    else
        k = k_new;
        Jold = Jnew;
    end
    [t, y] = ode45('ConcODE', [0 5], y0, []);

    y_hat = interp1(t,y,tspan);
    for n = 1:24
        tmp(n) =  (y_hat(n)-Ca_data(n))^2;
    end
    Jnew = 1/n*sum(tmp);


    dP = -learn_rate*(Jnew-Jold)/(k-k_old); %  k(+1) = k - LR(dJ/dK)
    
    k_old = k;
    k_new = k+dP;
    
    Ki(i) = k_new;
    Ji(i) = Jnew;
    
    if dP < 1e-6
        break
    end
end

hold on
plot(t,y)

figure, plot(Ki,Ji)

[Walter Roberson]

Unfortunately we cannot test without the .mat

[Torsten]

1. y0 must be a 2-element vector
2. The ODE you gave in the text and the one used in the code seem to differ.

Try

https://www.wolframalpha.com/input/?i=y''(t)+%2B+b*y'(t)+%2B+k%2Fm*y(t)+%3D+0

to solve your ODE analytically first and then use lsqcurvefit to fit k to your data.