MATLAB: Change in velocity equation with explicit method

equationexplicitexplicit methodhelpMATLABmethod

Hello Everyone, I am new to MatLab, and looking for some help.
I have a code where I have 3600 time steps.
I am calculating change in mass of a rocket every step which is assumed to be constant (5000kg/s)
with this bit of a code 
for n=2:length(t)
    if M(n-1) >= mass_r;
        M(n)=M(n-1)-dm*dt;
    else
        M(n)=mass_r-1;
    end
end
I would like someone to help me to implement this equation in MatLab form
I tried using an explicit method but alot of errors just rainfalls on me.
Would appreciate any help.

Best Answer

See this solution by using ode45
[t, V] = ode45(@dV, [0 300], 0);
plot(t,V)
function dVdt = dV(t, V)
    G = 6.67408e-11;
    M = 5.9722e24;
    R = 6371e3;
    A = 75;
    Cd = 0.4;
    me = 54000;
    mo = 894000;
    ve = 4500;
    dmdt = 5000;
    
    m_fuel = mo - me;
    time_fuel = m_fuel/dmdt;
    
    if t < time_fuel
        m = mo - t*dmdt;
    else
        m = me;
    end
    
    dVdt = 1/m*(ve*dmdt - G*M*m/R^2 - 0.5*Cd*A*V^2);
end
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