2.1124   ODE No. 1124

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ -2 \left (x^2-a\right ) y'(x)+2 n x y(x)+x y''(x)=0 \] Mathematica : cpu = 0.0683357 (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 = 0.194 (sec), leaf count = 29

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