2.1516   ODE No. 1516

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

\[ x^3 y^{(3)}(x)+(x+3) x^2 y''(x)+5 (x-6) x y'(x)+(4 x+30) y(x)=0 \] Mathematica : cpu = 300.035 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.457 (sec), leaf count = 263

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {x}^{4}-84\,{x}^{3}+2016\,{x}^{2}-20160\,x+75600 \right ) }{{x}^{6}}}+{\frac {{\it \_C2}\,{{\rm e}^{-x}} \left ( {x}^{8}+28\,{x}^{7}+450\,{x}^{6}+5100\,{x}^{5}+42900\,{x}^{4}+267120\,{x}^{3}+1179360\,{x}^{2}+3326400\,x+4536000 \right ) }{{x}^{6}}}+{\frac {{\it \_C3}\, \left ( {{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{8}+28\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{7}+450\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{6}+5100\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{5}+{x}^{7}+42900\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{4}+29\,{x}^{6}+267120\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{3}+60\,{x}^{4}\ln \left ( x \right ) +480\,{x}^{5}+1179360\,{{\rm e}^{-x}}{x}^{2}{\it Ei} \left ( 1,-x \right ) -5040\,{x}^{3}\ln \left ( x \right ) +5612\,{x}^{4}+3326400\,{{\rm e}^{-x}}x{\it Ei} \left ( 1,-x \right ) +120960\,{x}^{2}\ln \left ( x \right ) +40152\,{x}^{3}+4536000\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) -1209600\,x\ln \left ( x \right ) +654192\,{x}^{2}+4536000\,\ln \left ( x \right ) -2761920\,x+27367200 \right ) }{{x}^{6}}} \right \} \]