ODE No. 1316

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

\[ x \left (x^2-1\right ) y''(x)+\left (x^2-1\right ) y'(x)-x y(x)=0 \] Mathematica : cpu = 0.0941704 (sec), leaf count = 38

\[\left \{\left \{y(x)\to c_2 G_{2,2}^{2,0}\left (x^2|\begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\\end {array}\right )+\frac {2 c_1 E\left (x^2\right )}{\pi }\right \}\right \}\] Maple : cpu = 0.047 (sec), leaf count = 18

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it EllipticE} \left ( x \right ) +{\it \_C2}\, \left ( {\it EllipticCE} \left ( x \right ) -{\it EllipticCK} \left ( x \right ) \right ) \right \} \]