# DSolve cannot solve for certain branches of the solution help pls

I get an error message while trying to compute this code.. help pls

    DSolve[{ A'[t] + 1/2 B[t]^2 a + ρ B[t] C[t] a + 1/2 a C[t]^2 == 0,
-B'[t] + 1/2 B[t]^2 b + ρ B[t] C[t] b + 1/2 b C[t]^2 == 1,
-C'[t] + 1/2 B[t]^2 c + ρ B[t] C[t] c + 1/2 c C[t]^2 == 0
A[T] == B[T] == C[T] == 0}, {A[t], B[t], C[t]},  t]


i get this "DSolve::bvfail: For some branches of the general solution, unable to solve the conditions."

why?

-
a) There is a missing comma after your third equation b) Don't start your symbols with uppercase letters c) C is a system-defined symbol d) DSolve[] doesn't seem able to solve that system –  belisarius Jan 30 '14 at 16:07
right, i just typed this in the forum. My main concern is part d) how to solve this analytically? –  user12091 Jan 31 '14 at 16:05
One way is to try for numerical values of parameters. If for all constants say, equal to one, Mma couldn't find a solution, there seems to be no sense trying the general case. At least before solving a concrete system. –  Andrew Jan 31 '14 at 17:00