complete the matlab function that numerically solves the above system of differential equations. initially p and h are zero whereas r0 = ξ·γ0 is the initial value for r. in matlab

To numerically solve a system of differential equations in MATLAB, you can use the ode45 function. Here's how you can complete the MATLAB function:

main.m
function solveDE()
    % Define the time span
    tspan = [0 10]; % Specify the time interval over which to solve the equations

    % Initial conditions
    p0 = 0;
    h0 = 0;
    r0 = xi * gamma0; % Initial value for r

    % Solve the system of differential equations
    [t, y] = ode45(@derivatives, tspan, [p0, h0, r0]);

    % Plot the results
    plot(t, y);
    legend('p(t)', 'h(t)', 'r(t)');
    xlabel('Time');
    ylabel('Values');
end

function dydt = derivatives(t, y)
    % Parameters
    xi = 0.1;
    gamma0 = 0.2;

    % System of differential equations
    dydt = zeros(3,1);
    dydt(1) = % Your equation involving p, h, and r here
    dydt(2) = % Your equation involving p, h, and r here
    dydt(3) = % Your equation involving p, h, and r here
end
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In the derivatives function, you need to define the system of differential equations that you want to solve. Fill in the equations for dydt(1), dydt(2), and dydt(3) based on the problem statement.

You can run the solveDE function in MATLAB to solve the system of differential equations numerically.

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