I am to find the solution $R(\rho)$ to the following differential equation,
$\frac{\partial}{\partial\rho}\left(A^2\frac{\partial}{\partial\rho}R(\rho)\right)-l(l+1)R(\rho)=0$
where $A$ is a numerically inverted function of $\rho$. My code is,
rho[r_, b_, q_] := (2 b/(1 - q)) (1 - (b/r)^(1 - q))^(1/2) Hypergeometric2F1[1/2, 1 - 1/(q - 1), 3/2, 1 - (b/r)^(1 - q)]
Tp = InverseFunction[Function[{r, b, q}, rho[r, b, q]], 1, 3];
ode = {D[(Tp[\[Rho], 0, -1])^2 D[R[\[Rho]], \[Rho]], \[Rho]] - l (l + 1)R[ [Rho]] + 2 \[Xi] a^2/(\[Rho]^2 + a^2) R[\[Rho]] == 0};
Bc = {R[0] == 1, R'[0] == 1};
rules = {AccuracyGoal -> Infinity, PrecisionGoal -> 20, WorkingPrecision -> 30, MaxSteps -> 10000};
Rsol = R /. First@NDSolve[Union[ode, Bc], {R}, {\[Rho], 0, 10}, rules]
This is what Mathematica says:
I don't know what is wrong with my code.