\[ x^3 y^{(3)}(x)-2 x^3+x^2 y''(x)+2 x y'(x)-y(x)+\log (x)=0 \] ✓ Mathematica : cpu = 0.40514 (sec), leaf count = 1656
\[\left \{\left \{y(x)\to c_3 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]}+c_1 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]}+\frac {\left (-2447+\left (884-340 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]+99 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]^2\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]+\left (147-721 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]-93 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]^2\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ] \left (757+1398 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]+\left (-1129+2149 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]+523 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]^2\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2\right )+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]^2 \left (470-1794 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]+1581 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ] \left (-1502+3905 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]-4526 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2\right )\right )\right ) \log (x)+\frac {72160 x^3-2 \left (5199 x^3+9833\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2+\left (6413-49216 x^3\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]^2 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2+\left (47228 x^3+39905\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ] \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2+\left (56108 x^3-81399\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]^2 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2+\left (2142 x^3+79343\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ] \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2+\left (7942 x^3+85\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]-2 \left (46379 x^3+51546\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]+2 \left (115687 x^3-67461\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]^2 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]+\left (444852 x^3-486021\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ] \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]-8 \left (2080 x^3-3773\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]^2 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]+\left (551538 x^3-557355\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ] \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]+\left (59119-91060 x^3\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]^2+2 \left (101430 x^3-63701\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ] \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]^2+2 \left (187565-285533 x^3\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]+1087 \left (36 x^3-25\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]+\frac {665867-605784 x^3}{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]}+\frac {469041-364360 x^3}{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]}-51016}{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ] \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]}}{\left (2-5 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]^2\right ) \left (\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]-\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]\right ) \left (-3+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]^2 \left (\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]-\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]-\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]\right ) \left (-3+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]\right ) \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2 \left (-2+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]\right )^2 \left (1+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]\right ) \left (-3+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]^2+2 \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ] \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]\right )}\right \}\right \}\]
✓ Maple : cpu = 0.519 (sec), leaf count = 866
\[ \left \{ y \left ( x \right ) =-\int \!-{\frac { \left ( {x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{1200}}+{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{12}}+{\frac {2}{3}}} \right ) ^{2}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \left ( -\ln \left ( x \right ) +2\,{x}^{3} \right ) \sqrt {3}\sqrt {23}}{13800\,{x}^{3}} \left ( \left ( \cos \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) \right ) ^{2}+ \left ( \sin \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) \right ) ^{2} \right ) }\,{\rm d}x{x}^{{\frac { \left ( -11+3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{600}}-{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{6}}+{\frac {2}{3}}}+ \left ( \int \!-{\frac {{x}^{{\frac { \left ( -11+3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{600}}-{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{6}}+{\frac {2}{3}}}{x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{1200}}+{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{12}}+{\frac {2}{3}}}\sqrt [3]{44+12\,\sqrt {69}}\sqrt {23}}{2300\,{x}^{3}} \left ( \left ( {\frac {100}{3}}+ \left ( \sqrt {69}-{\frac {11}{3}} \right ) \sqrt [3]{44+12\,\sqrt {69}} \right ) \sqrt {3}\cos \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) -3\,\sin \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) \left ( -{\frac {100}{3}}+ \left ( \sqrt {69}-11/3 \right ) \sqrt [3]{44+12\,\sqrt {69}} \right ) \right ) \left ( {x}^{3}-{\frac {\ln \left ( x \right ) }{2}} \right ) }\,{\rm d}x+{\it \_C2} \right ) {x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{1200}}+{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{12}}+{\frac {2}{3}}}\cos \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) + \left ( \int \!-{\frac {3\,{x}^{{\frac { \left ( -11+3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{2/3}}{600}}-1/6\,\sqrt [3]{44+12\,\sqrt {69}}+2/3}{x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{2/3}}{1200}}+1/12\,\sqrt [3]{44+12\,\sqrt {69}}+2/3}\sqrt [3]{44+12\,\sqrt {69}}\sqrt {23}}{2300\,{x}^{3}} \left ( \left ( -{\frac {100}{3}}+ \left ( \sqrt {69}-{\frac {11}{3}} \right ) \sqrt [3]{44+12\,\sqrt {69}} \right ) \cos \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) +{\frac { \left ( {\frac {100}{3}}+ \left ( \sqrt {69}-{\frac {11}{3}} \right ) \sqrt [3]{44+12\,\sqrt {69}} \right ) \sqrt {3}}{3}\sin \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) } \right ) \left ( {x}^{3}-{\frac {\ln \left ( x \right ) }{2}} \right ) }\,{\rm d}x+{\it \_C3} \right ) {x}^{{\frac { \left ( 11-3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{1200}}+{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{12}}+{\frac {2}{3}}}\sin \left ( {\frac {\sqrt {3}\sqrt [3]{44+12\,\sqrt {69}} \left ( 3\,\sqrt {69}\sqrt [3]{44+12\,\sqrt {69}}-11\,\sqrt [3]{44+12\,\sqrt {69}}+100 \right ) \ln \left ( x \right ) }{1200}} \right ) +{\it \_C1}\,{x}^{{\frac { \left ( -11+3\,\sqrt {69} \right ) \left ( 44+12\,\sqrt {69} \right ) ^{{\frac {2}{3}}}}{600}}-{\frac {\sqrt [3]{44+12\,\sqrt {69}}}{6}}+{\frac {2}{3}}} \right \} \]