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 = 0.157462 (sec), leaf count = 26
\[\{\{y(x)\to c_2 D_{-a-1}(i x)+c_1 D_a(x)\}\}\]
Maple ✓
cpu = 0.618 (sec), leaf count = 39
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \WhittakerM \left (\frac {a}{2}+\frac {1}{4}, \frac {1}{4}, \frac {x^{2}}{2}\right )}{\sqrt {x}}+\frac {\textit {\_C2} \WhittakerW \left (\frac {a}{2}+\frac {1}{4}, \frac {1}{4}, \frac {x^{2}}{2}\right )}{\sqrt {x}}\right ]\] 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))
Maple raw output
[y(x) = _C1/x^(1/2)*WhittakerM(1/2*a+1/4,1/4,1/2*x^2)+_C2/x^(1/2)*WhittakerW(1/2*a+1/4,1/4,1/2*x^2)]