MATLAB is not powerful enough to solve that analytically. Maple says that the solution is
f1(x) = -(1/2)*exp(1i*omg*t)*(C2*(1i*k-(-k^2-4*A^2*g+(4i)*k*l+4*l^2)^(1/2)+2*l)*exp((1/2)*(1i*k-(-k^2-4*A^2*g+(4i)*k*l+4*l^2)^(1/2))*x)+C1*exp((1/2)*(1i*k+(-k^2-4*A^2*g+(4i)*k*l+4*l^2)^(1/2))*x)*(1i*k+(-k^2-4*A^2*g+(4i)*k*l+4*l^2)^(1/2)+2*l))/(g^(1/2)*exp(i*k*x)*A)
f2(x) = C1*exp((1/2)*(1i*k+(-k^2-4*A^2*g+(4*1i)*k*l+4*l^2)^(1/2))*x)+C2*exp((1/2)*(1i*k-(-k^2-4*A^2*g+(4*1i)*k*l+4*l^2)^(1/2))*x)
Here, C1 and C2 are arbitrary constants of integration that depend upon the boundary conditions.
