performance tuning - DSolve gets stuck on system of differential equations with unassigned variable

Hopefully someone can help me with this problem. I'm running a fairly simple script that involves some matrix operations and ends with a fairly nasty system of differential equations:

h2 = {{0, -(Ω/2)}, {-(Ω/2), -k v + Δ}}

ρ = {{ρ11[t], ρ12[t]}, {ρ21[t], ρ22[t]}}


ρprime = -I (h2.ρ - ρ.h2) + {{1/2 γ ρ22[t], -γ ρ12[t]}, {-γ ρ21[t], -(1/2) γ ρ22[t]}}

replace3 = {Δ -> 0.1, γ -> 1, Ω -> 0.1, k -> 0.1}; 

p3 = DSolve[{ρ11'[t] == ρprime[[1, 1]], ρ12'[t] == ρprime[[1, 2]], 
             ρ21'[t] == ρprime[[2, 1]], ρ22'[t] == ρprime[[2, 2]], 
             ρ11[0] == 1, ρ22[0] == 0, ρ12[0] == 0, ρ21[0] == 0} /. replace3, 
            {ρ11[t], ρ12[t], ρ21[t], ρ22[t]}, {t}]

Basically, I'm trying to solve a system of four differential equations analytically, with one variable, v, left unassigned. It is very important that v not be assigned a value as this point in the script. However, when I run it, it gets stuck on the DSolve part and can't seem to do it. When I first assign v a value and then run it, the DSolve works fine. Is this system of equations simply to complicated to be solved analytically? Is there another way to do this?