2.1124   ODE No. 1124

\[ -2 \left (x^2-a\right ) y'(x)+2 n x y(x)+x y''(x)=0 \] Mathematica : cpu = 0.0617711 (sec), leaf count = 65


\[\left \{\left \{y(x)\to c_1 \, _1F_1\left (-\frac {n}{2};a+\frac {1}{2};x^2\right )+i^{1-2 a} c_2 x^{1-2 a} \, _1F_1\left (-a-\frac {n}{2}+\frac {1}{2};\frac {3}{2}-a;x^2\right )\right \}\right \}\] Maple : cpu = 0.082 (sec), leaf count = 29


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