2.1450   ODE No. 1450

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

\[ a x^3 y(x)-b x+y^{(3)}(x)=0 \] Mathematica : cpu = 300.008 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.363 (sec), leaf count = 2294

\[ \left \{ y \left ( x \right ) =\int \!1401400\,{b{x}^{3} \left ( 8\,{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}})}-5\,{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}a+280\,{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \right ) \left ( -1100\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}+5096\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}+1400\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}-3185\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+1925\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}-3920\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}+400400\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+1121120\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}-1401400\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+38500\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{a}^{2}-156800\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}{a}^{2}+178360\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+134534400\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\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}})}-63063000\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}a-58858800\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+784784000\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \right ) ^{-1}}\,{\rm d}x{\mbox {$_0$F$_2$}(\ ;\,{\frac {2}{3}},{\frac {5}{6}};\,-{\frac {{x}^{6}a}{216}})}+\int \!1401400\,{b{x}^{2} \left ( 5\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}a-14\,{x}^{6}{\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}})}a-560\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \right ) \left ( -1100\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}+5096\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}+1400\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}-3185\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+1925\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}-3920\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}+400400\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+1121120\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}-1401400\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+38500\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{a}^{2}-156800\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}{a}^{2}+178360\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+134534400\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\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}})}-63063000\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}a-58858800\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+784784000\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \right ) ^{-1}}\,{\rm d}xx{\mbox {$_0$F$_2$}(\ ;\,{\frac {5}{6}},{\frac {7}{6}};\,-{\frac {{x}^{6}a}{216}})}+\int \!-2802800\,{bx \left ( 4\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}a-7\,{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-140\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})} \right ) \left ( -1100\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}+5096\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}+1400\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}-3185\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+1925\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}-3920\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{18}{a}^{3}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}+400400\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+1121120\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {11}{6}},{\frac {13}{6}};\,-{\frac {{x}^{6}a}{216}})}-1401400\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}+38500\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,{\frac {19}{6}},10/3;\,-{\frac {{x}^{6}a}{216}})}{a}^{2}-156800\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,{\frac {17}{6}},{\frac {19}{6}};\,-{\frac {{x}^{6}a}{216}})}{a}^{2}+178360\,{\mbox {$_0$F$_2$}(\ ;\,8/3,{\frac {17}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{12}{a}^{2}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+134534400\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\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}})}-63063000\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{x}^{6}{\mbox {$_0$F$_2$}(\ ;\,{\frac {13}{6}},7/3;\,-{\frac {{x}^{6}a}{216}})}a-58858800\,{\mbox {$_0$F$_2$}(\ ;\,5/3,{\frac {11}{6}};\,-{\frac {{x}^{6}a}{216}})}{x}^{6}a{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})}+784784000\,{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {{x}^{6}a}{216}})}{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {{x}^{6}a}{216}})} \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 \} \]