# Solving system of differential equations without initial conditions

I have posted a question on math stackexchange (see here), where I have a system of differential equations, and all I have is the behavior of a variable as a power series.

That is, I have a specified fall off conditions at infinity. Then one needs to expand this in power series and look how the coefficients are behaving.

What I am wondering here, is something like this possible to solve with Mathematica?

I could set up a system of differential equations, setting my $\xi^r, \xi^t, \xi^\phi$ equal to some variables $A,B,C$ that depend on $(t,r,\phi)$, but all I could do is set the equations equal to zero, and not specify any initial condition. That would give me a lot of constants.

I also thought of numerically solving, but I really can't think how I could get anything useful there because I have no initial conditions.

If needed I'll expand this question further.

-