Explicit solution could not be found in a system of ODEs?

Hello I'm trying to model the next system of differential equations:

dg11/ dt = (r - (1 + 1) * c) * g11 * ( 1 - (g11 + g10 + g01 + g00) / K)

dg10/ dt = (r - (1 + 0) * c) * g10 * ( 1 - (g11 + g10 + g01 + g00) / K)

dg01/ dt = (r - (0 + 1) * c) * g01 * ( 1 - (g11 + g10 + g01 + g00) / K)

dg00/ dt = (r - (0 + 0) * c) * g00 * ( 1 - (g11 + g10 + g01 + g00) / K)

using dsolve but I got the next error message:

Warning: Explicit solution could not be found. 
> In dsolve (line 201)
In testmodel (line 38) 
Struct contents reference from a non-struct array object.

This is my code:

 syms g11(t) g10(t) g01(t) g00(t); 
r = 1;
c= 0.1;
k= 10000; 

 ode1 = diff(g11) == (r - (1 + 1) * c) * g11 * (1 - ((g11 + g10 + g01 + g00) / k));
ode2 = diff(g10) == (r - (1 + 0) * c) * g10 * (1 - ((g11 + g10 + g01 + g00) / k));
ode3 = diff(g01) == (r - (0 + 1) * c) * g01 * (1 - ((g11 + g10 + g01 + g00) / k));
ode4 = diff(g00) == (r - (0 + 0) * c) * g00 * (1 - ((g11 + g10 + g01 + g00) / k)); 
odes = [ode1; ode2; ode3; ode4];
S = dsolve(odes);

I tried changing the variables g11, g10...with numerical values and it works but with just the variables is not working. Any suggestions?

[Torsten]

Many ODE systems don't have explicit solutions - yours is one of them.

Best wishes

Torsten.