How to use ODE45 with two second order linear equation?

Hello MatLab!

I am currently learning how to use MatLab for a physics research project at my university. I tried writing my own RK45 script but I am not sure if the results I got make any sense, so I want to compare my results with those of ODE45. However, I am unsure how to give ODE45 four first order equations. The equations I want to use are the following,

function vdot = quad_drag_density(t,v)

% Here we will define our constants

m = 1; % Mass of a shell, in kg

g = 9.81; % Acceleration of gravity, in m/s

r = 0.15; % Radius of shell, in m

C_d = 0.4; % Coefficient of drag such that the % drag is proportional to the square % of the speed

A = pi*r^2; % Cross sectional area of shell, in % m^2

x_ddot = (-(1.22)*exp(-y(1)/8500)*C_d*A*sqrt(vx(1)^2 + vy(1)^2) ... *vx(1))/2*m;

y_ddot = - g - ((1.22)*exp(-y(1)/8500)*C_d*A*sqrt(vx(1)^2 ... + vy(1)^2)*vy(1))/2*m;

I spilt each into two first order equations as follows,

dz(1) = z(2);

dz(2) = (-(1.22)*exp(-z(3)/8500)*C_d*A*sqrt(z(2)^2 + z(4)^2) ... *z(2))/2*m;

dz(3) = z(4);

dz(4) = - g - ((1.22)*exp(-z(3)/8500)*C_d*A*sqrt(z(2)^2 ... + z(4)^2)*z(4))/2*m;

vdot = [dz(1); dz(2); dz(3), dz(4)];

and I do not know where to go from here, or if anything I did was correct up to here.

[Walter Roberson]

Duplicates http://uk.mathworks.com/matlabcentral/answers/256180-how-to-use-ode45-with-two-second-order-linear-equation