Ok thank you very much you are right, I did a stupid logical error...

But another problem appeared : 

although I entered :

assume(Gamma^2-2*beta*Gamma+beta^2-4*omega[0]^2<0);

when I execute 

dsolve(eq3); 

Maple returns me something with 

(Gamma^2-2*beta*Gamma+beta^2-4*omega[0]^2)^(1/2)

How is that possible ?

(I forgot to tick " E-mail me when new comments are added to this " in my first message, hence this one)