4.137   ODE No. 1137

\[ \boxed { 4\,x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +4\,y \left ( x \right ) - \left ( x+2 \right ) y \left ( x \right ) +ly \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.095512 (sec), leaf count = 74 \[ \left \{\left \{y(x)\to \frac {1}{4} c_2 e^{-x/2} x \, _1F_1\left (\frac {1}{128} (-32 (l+(2-4 i))-128 i)+1;2;x\right )+\frac {1}{4} c_1 e^{-x/2} x U\left (\frac {1}{128} (-32 (l+(2-4 i))-128 i)+1,2,x\right )\right \}\right \} \]

Maple: cpu = 0.109 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}_{{\frac {l}{4}}+{ \frac {1}{2}},\,{\frac {1}{2}}}\left (x\right )}+{\it \_C2}\,{{\sl W}_{{ \frac {l}{4}}+{\frac {1}{2}},\,{\frac {1}{2}}}\left (x\right )} \right \} \]