4.317   ODE No. 1317

\[ \boxed { x \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 3\,{x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +xy \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.115015 (sec), leaf count = 38 \[ \left \{\left \{y(x)\to c_2 G_{2,2}^{2,0}\left (x^2| \begin {array}{c} \frac {1}{2},\frac {1}{2} \\ 0,0 \\ \end {array} \right )+\frac {2 c_1 K\left (x^2\right )}{\pi }\right \}\right \} \]

Maple: cpu = 0.032 (sec), leaf count = 13 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it EllipticK} \left ( x \right ) +{\it \_C2}\,{\it EllipticCK} \left ( x \right ) \right \} \]