2.1275   ODE No. 1275

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

\[ y(x) \left (2 x (2 l-m+1)-m^2-x^2+1\right )+4 x^2 y''(x)+4 x y'(x)=0 \] Mathematica : cpu = 0.0355848 (sec), leaf count = 120

\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} \left (\sqrt {m^2-1} \log (x)-x\right )} U\left (\frac {1}{2} \left (-2 l+m+\sqrt {m^2-1}\right ),\sqrt {m^2-1}+1,x\right )+c_2 e^{\frac {1}{2} \left (\sqrt {m^2-1} \log (x)-x\right )} L_{\frac {1}{2} \left (2 l-\sqrt {m^2-1}-m\right )}^{\sqrt {m^2-1}}(x)\right \}\right \}\]

Maple : cpu = 0.524 (sec), leaf count = 55

\[ \left \{ y \left ( x \right ) ={{\it \_C1}{{\sl M}_{l-{\frac {m}{2}}+{\frac {1}{2}},\,{\frac {1}{2}\sqrt {m-1}\sqrt {m+1}}}\left (x\right )}{\frac {1}{\sqrt {x}}}}+{{\it \_C2}{{\sl W}_{l-{\frac {m}{2}}+{\frac {1}{2}},\,{\frac {1}{2}\sqrt {m-1}\sqrt {m+1}}}\left (x\right )}{\frac {1}{\sqrt {x}}}} \right \} \]