4.118   ODE No. 1118

\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( \left ( a+b \right ) x+m+n \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( abx+na+bm \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.093012 (sec), leaf count = 51 \[ \left \{\left \{y(x)\to c_1 e^{-a x} U(m,m+n,(a-b) x)+c_2 e^{-a x} L_{-m}^{m+n-1}(x (a-b))\right \}\right \} \]

Maple: cpu = 0.063 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-ax}}{{\sl M}\left ( m,\,m+n,\,x \left ( a-b \right ) \right )}+{\it \_C2}\,{{\rm e}^{-ax}}{ {\sl U}\left (m,\,m+n,\,x \left ( a-b \right ) \right )} \right \} \]