ODE
\[ \left (4 a-x^2+2\right ) y(x)+4 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00853339 (sec), leaf count = 26
\[\left \{\left \{y(x)\to c_1 D_a(x)+c_2 D_{-a-1}(i x)\right \}\right \}\]
Maple ✓
cpu = 0.126 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={1 \left ( {\it \_C2}\,{{\sl W}_{{\frac {a}{2}}+{\frac {1}{4}},\,{\frac {1}{4}}}\left ({\frac {{x}^{2}}{2}}\right )}+{\it \_C1}\,{{\sl M}_{{\frac {a}{2}}+{\frac {1}{4}},\,{\frac {1}{4}}}\left ({\frac {{x}^{2}}{2}}\right )} \right ) {\frac {1}{\sqrt {x}}}} \right \} \] 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)