4.1217   y(x)(a+ bcos(2x ))+ y′′(x) = 0

ODE

y(x)(a+ bcos(2x)) +y′′(x) = 0

ODE Classification

[_ellipsoidal]

Book solution method
TO DO

Mathematica
cpu = 0.025772 (sec), leaf count = 28

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

Maple
cpu = 0.396 (sec), leaf count = 21

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

Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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