Solving a system of differential equations (maybe with Mathematica?)

I have this coupled set of non-linear DE's which I would very much like to get a solution to:

$A_1 \dfrac{d}{dr}(r^3 \dfrac{d \xi_1}{dr}) - V_1 r^3 \xi_1 + V_2 \dfrac{d}{dr}(r^5 \dfrac{d \xi_1}{dr}) + V_4 \dfrac{d}{dr}(r^4 \dfrac{d \xi_2}{dr}) + V_5 \dfrac{d}{dr}(r^3 \xi_2) = 0$

and

$\dfrac{d}{dr} (r^3 \dfrac{d \xi_2}{dr}) - r \xi_2 + T_1 \dfrac{d}{dr}(r^3 \dfrac{d \xi_1}{dr}) + T_2 r^2 \dfrac{d \xi_1}{dr}$

Some thoughts: apart from that one term at the beginning of equation 1, the system is equidimensional and probably has a solution of the form r^k for some k. However, as it is, we probably don't have a solution of that form.

I've tried putting this into Mathematica by defining

system = {D[r^3*x'[r],r] - r^3*x [r] + D[r^5*x'[r], r] + D[r^4*y'[r], r] + D[r^3*y'[r], r] == 0, D[r^3*y'[r], r] - r*y[r] + D[r^3*x'[r], r] + r^2*x'[r] == 0}

(here I've ignored constants for the time being, and set xi_1 and xi_2 to be x and y).

But when I try and use DSolve on it (ie DSolve[system, {x,y}, r]) I just get the input back as the output. Is this Mathematica's way of saying the system is insoluble?