Using dsolve to solve a system of differential equations analytically

When trying to solve a system analytically using dsolve, Matlab outputs that x is an empty function handle. Can someone explain why the following code does not work as expected?

m                     = 3.125*0.001;                   % Mass of the body in slug
Cd                   = 4.71*10^-7;                   
g = 32.2;    
syms x(t) y(t)                                      
Dx = diff(x,1);                                    
D2x = diff(x,2);                                    
Dy = diff(y,1);                                  
D2y = diff(y,2);                                  
[x,y] = dsolve([-Cd*Dx*sqrt(Dx^2+Dy^2)==m*D2x,-Cd*Dy*sqrt(Dx^2+Dy^2)-m*g==m*D2y],...
                  [x(0)==0  ,Dx(0)== 186*8.8/6*cosd(11.2), y(0) == 0, Dy(0)==186*8.8/6*sind(11.2)], 't');  
x
x = matlabFunction(x)   

Answer 1

[Star Strider]

The differential equation system is nonlinear, so it likely does not have an analytic solution.

Try this instead:

m                     = 3.125*0.001;                   % Mass of the body in slug
Cd                   = 4.71*10^-7;                   
g = 32.2;    
syms x(t) y(t) T Y                                      
Dx = diff(x,1);                                    
D2x = diff(x,2);                                    
Dy = diff(y,1);                                  
D2y = diff(y,2);                                  
[VF,Sbs] = odeToVectorField([-Cd*Dx*sqrt(Dx^2+Dy^2)==m*D2x,-Cd*Dy*sqrt(Dx^2+Dy^2)-m*g==m*D2y],...
                  [x(0)==0  ,Dx(0)== 186*8.8/6*cosd(11.2), y(0) == 0, Dy(0)==186*8.8/6*sind(11.2)]);  

Fcn = matlabFunction(VF, 'Vars',{T,Y});

[T,Y] = ode45(Fcn, [0 10], [0 0 0 1]); 

figure
plot(T, Y)
grid
legend(string(Sbs), 'Location','SW')

.

[Aleem Andrew]

Thanks for your help

[Star Strider]

As always, my pleasure!