2.1239   ODE No. 1239

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

\[ -l y(x)+\left (x^2-1\right ) y''(x)+2 x y'(x)=0 \] Mathematica : cpu = 0.0102734 (sec), leaf count = 46

\[\left \{\left \{y(x)\to c_1 P_{\frac {1}{2} \left (\sqrt {4 l+1}-1\right )}(x)+c_2 Q_{\frac {1}{2} \left (\sqrt {4 l+1}-1\right )}(x)\right \}\right \}\] Maple : cpu = 0.249 (sec), leaf count = 35

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it LegendreP} \left ( {\frac {1}{2}\sqrt {1+4\,l}}-{\frac {1}{2}},x \right ) +{\it \_C2}\,{\it LegendreQ} \left ( {\frac {1}{2}\sqrt {1+4\,l}}-{\frac {1}{2}},x \right ) \right \} \]