2.1048   ODE No. 1048

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

\[ \left (2 n+3 x^2-1\right ) y(x)+y''(x)-4 x y'(x)=0 \] Mathematica : cpu = 0.0095042 (sec), leaf count = 45

\[\left \{\left \{y(x)\to c_1 e^{\frac {x^2}{2}} H_n(x)+c_2 e^{\frac {x^2}{2}} \, _1F_1\left (-\frac {n}{2};\frac {1}{2};x^2\right )\right \}\right \}\] Maple : cpu = 0.129 (sec), leaf count = 37

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