Unable to perform assignment because the left and right sides have a different number of elements

Error appears in Line 41 according to Matlab. I believe it has something to do with putting a matrix as phi_0 into y_dot(2). Can anyone give some advice on how to correct this?

% ode45

% 1. Define Initial Conditions

x_0 = 50*pi/180*randn(2,50);

phi_0 = x_0(1,:);

phi_dot_0 = x_0(2,:);

y_0 = [phi_0; phi_dot_0]; % Initial State Vector

% 2. Initialize Temporal Parameters

t_0 = 0;

t_f = 10; % sec

tspan = [0 10];

% 3. ode45

options = odeset('RelTol', 10^(-12), 'AbsTol', 10^(-12)); % the tolerances tell ode45 how "accurate to be

[t, X] = ode45(@project, tspan, x_0, options);

plot (t, X(:,1)');

%% %% FUNCTIONS %% %%

function y_dot = project(t,y)

%Initialize

y_dot = zeros(2,50);

x_0 = 50*pi/180*randn(2,50);

phi_0 = x_0(1,:);

%Parameters

g = 9.81;

L1 = 0.5;

L2 = 0.5;

omega = 0.5*sqrt(g/L2);

%State Space Representation of System

y_dot(1) = y(2);

y_dot(2) = ((2*(omega.^2)*(cos(phi_0).^2))-(omega.^2)-(g*cos(phi_0)/L2))*y(1);

end

Answer 1

[Alan Stevens]

Like this?

   % 1. Define Initial Conditions
        N = 50;  % 
        x_0 = 50*pi/180*randn(2,N);
        phi_0 = x_0(1,:);
        phi_dot_0 = x_0(2,:);
        y_0 = [phi_0; phi_dot_0]; % Initial State Vector
    % 2. Initialize Temporal Parameters
        t_0 = 0;
        t_f = 10; % sec
        tspan = [0 10];
    % 3. ode45
        options = odeset('RelTol', 10^(-12), 'AbsTol', 10^(-12));  % the tolerances tell ode45 how "accurate to be
        
        for i = 1:N   % Loop N times
        
        [t, X] = ode45(@project, tspan, y_0(:,i), options);
        
        plot (t, X(:,1));  % Assumes you want all 50 plotted on the same graph
        hold on
        end
        grid
        xlabel('t'), ylabel('\phi')
        
%% %% FUNCTIONS %% %%
function y_dot = project(~,y)
   
    %Initialize
        y_dot = zeros(2,1);
        
    %Parameters
        g = 9.81;
       % L1 = 0.5;  
        L2 = 0.5;
        omega = 0.5*sqrt(g/L2);
    
    %State Space Representation of System
        y_dot(1) = y(2);
        y_dot(2) = ((2*(omega.^2)*(cos(y(1)).^2))-(omega.^2)-(g*cos(y(1))/L2))*y(1);
    
end