2.1052   ODE No. 1052

\[ a x y'(x)+b y(x)+y''(x)=0 \] Mathematica : cpu = 0.0152488 (sec), leaf count = 78


\[\left \{\left \{y(x)\to c_1 e^{-\frac {a x^2}{2}} H_{\frac {b-a}{a}}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )+c_2 e^{-\frac {a x^2}{2}} \, _1F_1\left (-\frac {b-a}{2 a};\frac {1}{2};\frac {a x^2}{2}\right )\right \}\right \}\] Maple : cpu = 0.083 (sec), leaf count = 58


\[y \relax (x ) = {\mathrm e}^{-\frac {a \,x^{2}}{2}} x \left (\KummerM \left (\frac {2 a -b}{2 a}, \frac {3}{2}, \frac {a \,x^{2}}{2}\right ) c_{1}+\KummerU \left (\frac {2 a -b}{2 a}, \frac {3}{2}, \frac {a \,x^{2}}{2}\right ) c_{2}\right )\]