4.1351   (4a− x2 + 2)y(x)+ 4y′′(x) = 0

ODE

(4a − x2 + 2)y(x)+ 4y′′(x ) = 0

ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.00853339 (sec), leaf count = 26

{{y(x) → c1Da(x)+ c2D−a− 1(ix)}}

Maple
cpu = 0.126 (sec), leaf count = 37

{        (           (   )             (   ))    }
           -    a 1 1  x2    -    a 1 1  x2   √1--
  y(x) = 1  C2W 2+4,4  2   + C1M  2+4,4  2      x

Mathematica raw input

DSolve[(2 + 4*a - x^2)*y[x] + 4*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[2]*ParabolicCylinderD[-1 - a, I*x] + C[1]*ParabolicCylinderD[a, x]}}

Maple raw input

dsolve(4*diff(diff(y(x),x),x)+(-x^2+4*a+2)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C2*WhittakerW(1/2*a+1/4,1/4,1/2*x^2)+_C1*WhittakerM(1/2*a+1/4,1/4,1/2*x
^2))/x^(1/2)