Thanks for your reply bigfooted,
I have been told I need to use hypergeometric solutions, (sorry for not mentioning this), but I have never seen them before. I have found the basic form of a hypergeometric series but I don't know how to apply this.
I have no idea how to start solving this ODE:
y''(x)+(μ^{2}*c(x)+k^{2})y=0
Where c(x)=A+Btanh(ρx) with constant A,B,ρ,μ,k
Could anyone give me a nudge in the right direction?
Cheers.