\[ \left (-a-x^2\right ) y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.005248 (sec), leaf count = 47
DSolve[(-a - x^2)*y[x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \operatorname {ParabolicCylinderD}\left (\frac {1}{2} (-a-1),\sqrt {2} x\right )+c_2 \operatorname {ParabolicCylinderD}\left (\frac {a-1}{2},i \sqrt {2} x\right )\right \}\right \}\] ✓ Maple : cpu = 0.112 (sec), leaf count = 29
dsolve(diff(diff(y(x),x),x)-(x^2+a)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {c_{1} \operatorname {WhittakerM}\left (-\frac {a}{4}, \frac {1}{4}, x^{2}\right )+c_{2} \operatorname {WhittakerW}\left (-\frac {a}{4}, \frac {1}{4}, x^{2}\right )}{\sqrt {x}}\]