2.1171   ODE No. 1171

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

\[ y(x) \left (a x+l x^2-n (n+1)\right )+x^2 y''(x)+2 x y'(x)=0 \] Mathematica : cpu = 0.056143 (sec), leaf count = 92

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

Maple : cpu = 0.122 (sec), leaf count = 49

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