5.78   ODE No. 1526

\[ \boxed { {x}^{2} \left ( {x}^{4}+2\,{x}^{2}+2\,x+1 \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( 2\,{x}^{6}+3\,{x}^{4}-6\,{x}^{2}-6\,x-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( {x}^{6}-6\,{x}^{3}-15\,{x}^{2}-12\,x-2 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( {x}^{4}+4\,{x}^{3}+8\,{x}^{2}+6\,x+1 \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]

Maple: cpu = 0.203 (sec), leaf count = 20 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{x}}+{\it \_C2}\,{ {\rm e}^{{x}^{-1}}}+{\it \_C3}\,x{{\rm e}^{x}} \right \} \]