ODE
\[ -a y(x)+y''(x)-x y'(x)=0 \] ODE Classification
[_Hermite]
Book solution method
TO DO
Mathematica ✓
cpu = 0.154003 (sec), leaf count = 39
\[\left \{\left \{y(x)\to c_1 H_{-a}\left (\frac {x}{\sqrt {2}}\right )+c_2 \, _1F_1\left (\frac {a}{2};\frac {1}{2};\frac {x^2}{2}\right )\right \}\right \}\]
Maple ✓
cpu = 0.46 (sec), leaf count = 35
\[\left [y \left (x \right ) = \textit {\_C1} \KummerM \left (\frac {a}{2}+\frac {1}{2}, \frac {3}{2}, \frac {x^{2}}{2}\right ) x +\textit {\_C2} \KummerU \left (\frac {a}{2}+\frac {1}{2}, \frac {3}{2}, \frac {x^{2}}{2}\right ) x\right ]\] Mathematica raw input
DSolve[-(a*y[x]) - x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*HermiteH[-a, x/Sqrt[2]] + C[2]*Hypergeometric1F1[a/2, 1/2, x^2/2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-x*diff(y(x),x)-a*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*KummerM(1/2*a+1/2,3/2,1/2*x^2)*x+_C2*KummerU(1/2*a+1/2,3/2,1/2*x^2)*x]