System of Second order order differential Equations referencing the 0th derivative

The following code refers to the system of differential equations in which only the first and second derivatives are included. How can the

zeroth derivative be referred to, for example, what if one of the equations was x'' = x*sqrt(x'^2+y'^2) rather than x'' = sqrt(x'^2+y'^2) - how could x be referred to? Writing

xy(0) for the 0th derivative or the position vector returns an error message but I am not sure how to modify the code. For example,

changing the first line to xy = zeros(6,1) does not help.

function xy=PackageMotion(t,x)
% the differential equation soltuion 
xy=zeros(4,1);

% The paramter of the package
m=1; g=9.82; Cd=0.035;

% The differential equation described in state space form

%xy(1)

xy(1)=x(2);                                 %first derivative (velocity)
xy(2)=(-Cd*x(2)*sqrt(x(2)^2+x(4)^2))/m;        
xy(3)=x(4);                                 
xy(4)=(-Cd*x(3)*sqrt(x(2)^2+x(4)^2))/m-g;     

end

[SL: formatted the text of the question as text rather than code]

[Walter Roberson]

If you have the symbolic toolbox, then I suggest following the steps in the first example in odeFunction

Answer 1

[Ameer Hamza]

For the state space system inside the PackageMotion function, the variables are in this order

x(1) -> x-position
x(2) -> x-veclcity
x(3) -> y-position
x(4) -> y-velocity

So your 2nd equation should be

xy(2)=(-Cd*x(1)*sqrt(x(2)^2+x(4)^2))/m;

See this example for more detail: https://www.mathworks.com/help/matlab/ref/ode45.html#bu3uj8b

[Aleem Andrew]

Thank you for your help