\[ x^3 y^{(3)}(x)+(x+3) x^2 y''(x)+5 (x-6) x y'(x)+(4 x+30) y(x)=0 \] ✗ Mathematica : cpu = 435.317 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f818}^{(3)}(\unicode {f817}) \unicode {f817}^3+(\unicode {f817}+3) \unicode {f818}''(\unicode {f817}) \unicode {f817}^2+5 (\unicode {f817}-6) \unicode {f818}'(\unicode {f817}) \unicode {f817}+(4 \unicode {f817}+30) \unicode {f818}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.467 (sec), leaf count = 263
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {x}^{4}-84\,{x}^{3}+2016\,{x}^{2}-20160\,x+75600 \right ) }{{x}^{6}}}+{\frac {{\it \_C2}\,{{\rm e}^{-x}} \left ( {x}^{8}+28\,{x}^{7}+450\,{x}^{6}+5100\,{x}^{5}+42900\,{x}^{4}+267120\,{x}^{3}+1179360\,{x}^{2}+3326400\,x+4536000 \right ) }{{x}^{6}}}+{\frac {{\it \_C3}\, \left ( {{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{8}+28\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{7}+450\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{6}+5100\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{5}+{x}^{7}+42900\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{4}+29\,{x}^{6}+60\,{x}^{4}\ln \left ( x \right ) +267120\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) {x}^{3}+480\,{x}^{5}-5040\,{x}^{3}\ln \left ( x \right ) +1179360\,{{\rm e}^{-x}}{x}^{2}{\it Ei} \left ( 1,-x \right ) +5612\,{x}^{4}+120960\,{x}^{2}\ln \left ( x \right ) +3326400\,{{\rm e}^{-x}}x{\it Ei} \left ( 1,-x \right ) +40152\,{x}^{3}-1209600\,x\ln \left ( x \right ) +4536000\,{{\rm e}^{-x}}{\it Ei} \left ( 1,-x \right ) +654192\,{x}^{2}+4536000\,\ln \left ( x \right ) -2761920\,x+27367200 \right ) }{{x}^{6}}} \right \} \]