I'm trying to solve an ODE with DSolve. The problem I'm facing is that in the ODE there appears an implicit function of the variable r*. The equation I'm trying to solve is
-q''[r*] + (-2 (a/r^3) (1 - a/r)^3 - w^2) q[r*] == 0
w parameters and
r*[r]=2 a Log[r-a]-a^2/(r-a)+r (tortoise coördinate), which cannot be inverted such that I cannot write my ODE only in terms of
r*. Is it possible to solve the equation by somehow using the implicit function relation?