The derivatives are uniformly 0, so the equations are constant, by definition. There is no reason to integrate them.
Try this:
syms d c EI q L
Eqs = [2*EI*(3*d*L^2+2*c*L)+q*L^3/4-q*L^3/3; 6*EI*(2*d*L^3+c*L^2)+q*L^4/5-q*L^4/3];
[c,d] = solve(Eqs, [c,d])
producing:
c =
(L^2*q)/(60*EI)
d =
(L*q)/(360*EI)
