Solve a system of two differential equations symbolically

Good evening, I'm trying to solve this system of two differential equations:

where r_x, r_y, alpha and beta are positive real parameters, by using this code:

syms x(t) y(t) rx ry alpha beta
ode1 = diff(x) == rx*x*(1-alpha*y);
ode2 = diff(y) == ry*y*(beta*x);
odes = [ode1; ode2];
S = dsolve(odes)
xSol(t) = S.x
ySol(t) = S.y

When I run the script, MATLAB returns me the following error:

Warning: Unable to find symbolic solution. 
> In dsolve (line 216)
  In [Name of the script] (line 59) 
 
S =
 
[ empty sym ]
 
Dot indexing is not supported for variables of this type.

Error in sym/subsref (line 898)
            R_tilde = builtin('subsref',L_tilde,Idx);

However, from what I've tried, it works if I change the original equations to this form:

and I run the code, but I need to solve the first ones, not these last.

Does anybody know how I can solve it?

Thanks in advance.

[Torsten]

No symbolic solution is possible for your set of equations.

Use a numerical integrator instead (e.g. ode15s).

[Conrado Santurino]

And do you know any other way to solve it symbolically? Because I have used Runge-Kutta 4 integrator to have a numerical solution, but I also need to find the symbolical expression. Thanks.

[Torsten]

predator-prey equations don't have an analytical solution.