4.1533   y(x)(a + bx2) +(1 − x2)y′′(x )− xy′(x) = 0

ODE

y(x)(a+ bx2)+ (1− x2)y′′(x)− xy′(x) = 0

ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0175672 (sec), leaf count = 42

{{                 [                 ]            [                 ]}}
                        b   b   −1                     b  b    −1
  y(x) → c1MathieuC a + 2,− 4,cos  (x) + c2MathieuS a + 2,−4 ,cos  (x)

Maple
cpu = 0.178 (sec), leaf count = 31

{                    (                 )               (                  )}
  y(x) =-C1M athieuC  b + a,− b,arccos(x ) +-C2M athieuS  b+ a,− b,arccos(x)
                      2      4                           2      4

Mathematica raw input

DSolve[(a + b*x^2)*y[x] - x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]*MathieuC[a + b/2, -b/4, ArcCos[x]] + C[2]*MathieuS[a + b/2, -b/4,
 ArcCos[x]]}}

Maple raw input

dsolve((-x^2+1)*diff(diff(y(x),x),x)-x*diff(y(x),x)+(b*x^2+a)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*MathieuC(1/2*b+a,-1/4*b,arccos(x))+_C2*MathieuS(1/2*b+a,-1/4*b,arccos
(x))