2.1044   ODE No. 1044

\[ -a y(x)+y''(x)-x y'(x)=0 \]

✓ Mathematica : cpu = 0.0061337 (sec), leaf count = 39

DSolve[-(a*y[x]) - x*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 H_{-a}\left (\frac {x}{\sqrt {2}}\right )+c_2 \, _1F_1\left (\frac {a}{2};\frac {1}{2};\frac {x^2}{2}\right )\right \}\right \}\]

✓ Maple : cpu = 0.129 (sec), leaf count = 35

dsolve(diff(diff(y(x),x),x)-x*diff(y(x),x)-a*y(x)=0,y(x))
 

\[y \left (x \right ) = x \left (\operatorname {KummerU}\left (\frac {1}{2}+\frac {a}{2}, \frac {3}{2}, \frac {x^{2}}{2}\right ) c_{2} +\operatorname {KummerM}\left (\frac {1}{2}+\frac {a}{2}, \frac {3}{2}, \frac {x^{2}}{2}\right ) c_{1} \right )\]