\[ \left (-a-x^2\right ) y(x)+4 y''(x)=0 \] ✓ Mathematica : cpu = 0.005426 (sec), leaf count = 36
DSolve[(-a - x^2)*y[x] + 4*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \operatorname {ParabolicCylinderD}\left (\frac {1}{4} (-a-2),x\right )+c_2 \operatorname {ParabolicCylinderD}\left (\frac {a-2}{4},i x\right )\right \}\right \}\] ✓ Maple : cpu = 0.115 (sec), leaf count = 33
dsolve(4*diff(diff(y(x),x),x)-(x^2+a)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {c_{2} \operatorname {WhittakerW}\left (-\frac {a}{8}, \frac {1}{4}, \frac {x^{2}}{2}\right )+c_{1} \operatorname {WhittakerM}\left (-\frac {a}{8}, \frac {1}{4}, \frac {x^{2}}{2}\right )}{\sqrt {x}}\]