\[ a x^3 y(x)-b x+y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 0.0723516 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{a \unicode {f818}(\unicode {f817}) \unicode {f817}^3-b \unicode {f817}+\unicode {f818}^{(3)}(\unicode {f817})=0,\unicode {f818}(0)=c_1,\unicode {f818}'(0)=c_2,\unicode {f818}''(0)=c_3\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.174 (sec), leaf count = 1616
\[ \left \{ y \left ( x \right ) =\int \!-11211200\,{b{x}^{3} \left ( \left ( -5/8\,{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}a+35\,{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}+{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}a{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \right ) \left ( \left ( \left ( -178360\,{a}^{2}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}+58858800\,{x}^{6}a{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}-784784000\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}-1925\,a \left ( \left ( 20\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a-32760\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}+ \left ( \left ( -{\frac {91\,{x}^{6}a}{55}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}}-728\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+a{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) a{x}^{6} \right ) {x}^{6} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}+1100\, \left ( \left ( \left ( {\frac {1568\,{x}^{6}a}{11}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}}-122304\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}-{\frac {1274\,{x}^{6}a}{275} \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a+220\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}-{\frac {10\,{x}^{6}a}{13}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}} \right ) } \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+ \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a-364\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}-{\frac {14\,{x}^{6}a}{11}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}} \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a \right ) {x}^{6}a \right ) ^{-1}}\,{\rm d}x{\mbox {$_0$F$_2$}(\ ;\,{\frac {2}{3}},{\frac {5}{6}};\,-{\frac {{x}^{6}a}{216}})}+\int \!-7007000\,{b{x}^{2} \left ( \left ( {x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}a-112\,{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}-{\frac {14\,{x}^{6}a}{5}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}} \right ) \left ( \left ( \left ( 156800\,{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}-134534400\,{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}a-784784000\,{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+1100\,{x}^{6}a \left ( \left ( -35\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a+57330\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}+ \left ( \left ( -{\frac {14\,{x}^{6}a}{11}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}}-364\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+a{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {x}^{6}a \right ) \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}-5096\,{x}^{6}a \left ( \left ( \left ( 35\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a-11550\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}+{x}^{6}a \left ( \left ( -{\frac {10\,{x}^{6}a}{13}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}}+220\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}+a{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+{\frac {275\,{x}^{6}a}{728} \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a-728\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}-{\frac {91\,{x}^{6}a}{55}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}} \right ) \right ) ^{-1}}\,{\rm d}xx{\mbox {$_0$F$_2$}(\ ;\,{\frac {5}{6}},{\frac {7}{6}};\,-{\frac {{x}^{6}a}{216}})}+\int \!11211200\,{bx \left ( \left ( {x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}a-35\,{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}-7/4\,{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}a \right ) \left ( \left ( \left ( -38500\,{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{a}^{2}+63063000\,{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}a-784784000\,{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}+1100\,{x}^{6}a \left ( \left ( {\frac {1568\,{x}^{6}a}{11}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}}-122304\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+ \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a-364\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}-{\frac {14\,{x}^{6}a}{11}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}} \right ) {x}^{6}a \right ) \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}-5096\,{x}^{6}a \left ( \left ( \left ( 35\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a-11550\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+{\frac {275\,{x}^{6}a}{728} \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a-728\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}-{\frac {91\,{x}^{6}a}{55}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}} \right ) } \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}+{x}^{6}a{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a+220\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}-{\frac {10\,{x}^{6}a}{13}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}} \right ) \right ) \right ) ^{-1}}\,{\rm d}x{x}^{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {7}{6}},{\frac {4}{3}};\,-{\frac {{x}^{6}a}{216}})}+{\it \_C1}\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {2}{3}},{\frac {5}{6}};\,-{\frac {{x}^{6}a}{216}})}+{\it \_C2}\,x{\mbox {$_0$F$_2$}(\ ;\,{\frac {5}{6}},{\frac {7}{6}};\,-{\frac {{x}^{6}a}{216}})}+{\it \_C3}\,{x}^{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {7}{6}},{\frac {4}{3}};\,-{\frac {{x}^{6}a}{216}})} \right \} \]