\[ a x y(x)-b+3 y''(x)+2 x y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 0.459929 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{-b+\unicode {f817} a \unicode {f818}(\unicode {f817})+3 \unicode {f818}''(\unicode {f817})+2 \unicode {f817} \unicode {f818}^{(3)}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.267 (sec), leaf count = 1616
\[ \left \{ y \left ( x \right ) =-\int \!2802800\,{bx \left ( \left ( -5/8\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}+{\frac {35}{4}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})}+{x}^{3}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}a \right ) \left ( \left ( \left ( -89180\,{a}^{2}{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {a{x}^{3}}{54}})}+7357350\,a{x}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})}-24524500\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}-3850\,a \left ( \left ( 5\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}-{\frac {4095}{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}} \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {a{x}^{3}}{54}})}+a \left ( \left ( -{\frac {91\,a{x}^{3}}{55}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {a{x}^{3}}{54}})}}-182\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}+a{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {a{x}^{3}}{54}})}{x}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})} \right ) {x}^{3} \right ) {x}^{3} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})}+2200\,a \left ( \left ( \left ( {\frac {392\,a{x}^{3}}{11}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {a{x}^{3}}{54}})}}-7644\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {a{x}^{3}}{54}})}-{\frac {1274\,a{x}^{3}}{275} \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}+55\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}-{\frac {10\,a{x}^{3}}{13}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})}} \right ) } \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}+a{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {a{x}^{3}}{54}})}{x}^{3} \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}-91\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}-{\frac {14\,a{x}^{3}}{11}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}} \right ) \right ) {x}^{3} \right ) ^{-1}}\,{\rm d}x{\mbox {$_0$F$_2$}(\ ;\,{\frac {2}{3}},{\frac {5}{6}};\,-{\frac {a{x}^{3}}{54}})}-\int \!-2802800\,{b \left ( \left ( {x}^{3}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}a-{\frac {35}{4}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})}} \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {a{x}^{3}}{54}})}-7/4\,{x}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})}a \right ) \left ( \left ( \left ( -19250\,{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {a{x}^{3}}{54}})}{x}^{6}+7882875\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}-24524500\,{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})}+2200\,a{x}^{3} \left ( \left ( {\frac {392\,a{x}^{3}}{11}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {a{x}^{3}}{54}})}}-7644\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}+a{x}^{3} \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}-91\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}-{\frac {14\,a{x}^{3}}{11}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}} \right ) \right ) \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {a{x}^{3}}{54}})}-10192\,a{x}^{3} \left ( \left ( \left ( {\frac {35\,a{x}^{3}}{4}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {a{x}^{3}}{54}})}}-{\frac {5775}{8}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})}} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}+{\frac {275\,a{x}^{3}}{728} \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}-182\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})}-{\frac {91\,a{x}^{3}}{55}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}} \right ) } \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})}+a \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}+55\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}-{\frac {10\,a{x}^{3}}{13}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})}} \right ) {x}^{3}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})} \right ) \right ) ^{-1}}\,{\rm d}x{\mbox {$_0$F$_2$}(\ ;\,{\frac {7}{6}},{\frac {4}{3}};\,-{\frac {a{x}^{3}}{54}})}x-\int \!-1751750\,{\sqrt {x}b \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}-28\,{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {a{x}^{3}}{54}})}-{\frac {14\,a{x}^{3}}{5}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})}} \right ) \left ( \left ( \left ( -78400\,{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {a{x}^{3}}{54}})}{x}^{6}+16816800\,{x}^{3}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}a+24524500\,{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}+19250\,a \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}-{\frac {819}{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}} \right ) {x}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})}+2800\,{a}^{2}{x}^{6} \left ( \left ( {\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}+{\frac {143}{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}} \right ) {\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})}-{\frac {11\,a{x}^{3}}{14}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {a{x}^{3}}{54}})}} \right ) \right ) {\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {a{x}^{3}}{54}})}-6370\,a{x}^{3} \left ( \left ( \left ( -14\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {a{x}^{3}}{54}})}a{x}^{3}+1155\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})}-8/5\,a \left ( \left ( -{\frac {10\,a{x}^{3}}{13}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {a{x}^{3}}{54}})}}+55\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})}+a{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {a{x}^{3}}{54}})}{x}^{3}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {a{x}^{3}}{54}})} \right ) {x}^{3} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}+a{x}^{3} \left ( \left ( -{\frac {55\,a{x}^{3}}{91}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {a{x}^{3}}{54}})}}+110\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {a{x}^{3}}{54}})}+a{x}^{3}{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {a{x}^{3}}{54}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {a{x}^{3}}{54}})} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})} \right ) \right ) ^{-1}}\,{\rm d}x\sqrt {x}{\mbox {$_0$F$_2$}(\ ;\,{\frac {5}{6}},{\frac {7}{6}};\,-{\frac {a{x}^{3}}{54}})}+{\it \_C1}\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {2}{3}},{\frac {5}{6}};\,-{\frac {a{x}^{3}}{54}})}+{\it \_C2}\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {7}{6}},{\frac {4}{3}};\,-{\frac {a{x}^{3}}{54}})}x+{\it \_C3}\,\sqrt {x}{\mbox {$_0$F$_2$}(\ ;\,{\frac {5}{6}},{\frac {7}{6}};\,-{\frac {a{x}^{3}}{54}})} \right \} \]