Question: ODE IVP

My problem is that Maple does not give answer at all for the initial value problem, so I need a help. If does exist a solution how can I obtain it?

Thanks in advance,  Sandor

infolevel[dsolve]:=5;
                                      5


ode:=(1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x$1)-(k^2/(1-x^2)-j*(j+1))*y(x)=0;

IcsEredeti:=y(1)=1,D(y)(1)=1;

                            y(1) = 1, D(y)(1) = 1
dsolve(ode);

Methods for second order ODEs:
--- Trying classification methods ---
trying a quadrature
checking if the LODE has constant coefficients
checking if the LODE is of Euler type
trying a symmetry of the form [xi=0, eta=F(x)]
   testing BRANCH 1 ->
   testing BRANCH 2 ->
   testing BRANCH 3 ->
   testing BRANCH 4 ->
   testing BRANCH 5 ->
   testing BRANCH 6 ->
checking if the LODE is missing 'y'
-> Trying a Liouvillian solution using Kovacic's algorithm
<- No Liouvillian solutions exists
-> Trying a solution in terms of special functions:
   -> Bessel
   -> elliptic
   -> Legendre
   <- Legendre successful
<- special function solution successful


          y(x) = _C1 LegendreP(j, k, x) + _C2 LegendreQ(j, k, x)
dsolve({ode,IcsEredeti});


Methods for second order ODEs:
--- Trying classification methods ---
trying a quadrature
checking if the LODE has constant coefficients
checking if the LODE is of Euler type
trying a symmetry of the form [xi=0, eta=F(x)]
checking if the LODE is missing 'y'
-> Trying a Liouvillian solution using Kovacic's algorithm
<- No Liouvillian solutions exists
-> Trying a solution in terms of special functions:
   -> Bessel
   -> elliptic
   -> Legendre
   <- Legendre successful
<- special function solution successful
Methods for second order ODEs:
--- Trying classification methods ---
trying a quadrature
checking if the LODE has constant coefficients
checking if the LODE is of Euler type
trying a symmetry of the form [xi=0, eta=F(x)]
checking if the LODE is missing 'y'
-> Trying a Liouvillian solution using Kovacic's algorithm
<- No Liouvillian solutions exists
-> Trying a solution in terms of special functions:
   -> Bessel
   -> elliptic
   -> Legendre
   <- Legendre successful
<- special function solution successful

 

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