Graph differential equations of parabolic trajectory affected by drag force

I cannot graph the solution to the following system of differential equations.

mx¨ = −C*x*sqrt(x˙^2 + y˙^2)

my¨ = −C*y* sqrt(x˙^2 + y˙^2)− mg

Initial conditions: x(0) = 0; y(0) = 0; C: 4*10^-7 (constant)

x˙ : first derivative of x position

x¨: second derivative of x position

y˙^2: square of first derivative of y position

I have tried the following code.

syms x(t) y(t)

t0 = 0;

tf = 5400;

dx=diff(x,t);

dy=diff(y,t);

eq1 = diff(x,2) == 2* dy;

eq2 = diff(y,2) == -2* dx;

vars = [x(t); y(t)];

V = odeToVectorField([eq1,eq2])

M = matlabFunction(V,'vars', {'t','Y'});

interval = [t0 tf];

ySol = ode45(M,interval,y0);

tValues = linspace(interval(1),interval(2),1000);

yValues = deval(ySol,tValues,1);

plot(tValues,yValues)

[Star Strider]

Thsi works for me:

syms x(t) y(t)
t0 = 0; 
tf = 5400; 
dx=diff(x,t);
dy=diff(y,t);
eq1 = diff(x,2) == 2* dy;
eq2 = diff(y,2) == -2* dx;
vars = [x(t); y(t)];
[V,S] = odeToVectorField([eq1,eq2])
M = matlabFunction(V,'vars', {'t','Y'});
interval = [t0 tf];   
y0 = [0 0 0 1];
ySol = ode45(M,interval,y0);
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1);  
plot(tValues,yValues) 

The only difference being that I provided a vector of initial values for ‘y0’, missing in your posted code.

[Aleem Andrew]

Thank you for your response

[Star Strider]

My pleasure.