ODE No. 1482

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

\[ a x y(x)-b+2 x y^{(3)}(x)+3 y''(x)=0 \] ✓ Mathematica : cpu = 2980.36 (sec), leaf count = 3626

\[\left \{\left \{y(x)\to c_1 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {a x^3}{54}\right )+\frac {\sqrt [6]{a} \sqrt {x} c_2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {a x^3}{54}\right )}{\sqrt [6]{2} \sqrt {3}}+\frac {\sqrt [3]{a} x c_3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {a x^3}{54}\right )}{3 \sqrt [3]{2}}+\frac {1}{6} \left (6 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {a x^3}{54}\right ) \int _1^x \frac {350350 \left (-8 a b \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^4+5 a b \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[1]^3\right ) K[1]^4-70 b \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right ) K[1]\right )}{-10192 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^9+6370 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^9+7840 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^9-2800 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^9-3850 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{54} a K[1]^3\right ) K[1]^9+2200 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{54} a K[1]^3\right ) K[1]^9-560560 a^2 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^6+700700 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[1]^3\right ) K[1]^6-200200 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[1]^3\right ) K[1]^6-89180 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^6+78400 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^6-19250 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{54} a K[1]^3\right ) K[1]^6+7357350 a \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^3-16816800 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[1]^3\right ) K[1]^3+7882875 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[1]^3\right ) K[1]^3-24524500 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[1]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[1]^3\right )} \, dK[1]+2^{5/6} \sqrt {3} \sqrt [6]{a} \sqrt {x} \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {a x^3}{54}\right ) \int _1^x \frac {350350 \sqrt [6]{2} \sqrt {3} b \left (-14 a \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^{7/2}+5 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[2]^3\right ) K[2]^{7/2}-140 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right ) \sqrt {K[2]}\right )}{\sqrt [6]{a} \left (10192 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^9-6370 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^9-7840 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^9+2800 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^9+3850 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{54} a K[2]^3\right ) K[2]^9-2200 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{54} a K[2]^3\right ) K[2]^9+560560 a^2 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^6-700700 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[2]^3\right ) K[2]^6+200200 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[2]^3\right ) K[2]^6+89180 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^6-78400 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^6+19250 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{54} a K[2]^3\right ) K[2]^6-7357350 a \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^3+16816800 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[2]^3\right ) K[2]^3-7882875 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[2]^3\right ) K[2]^3+24524500 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[2]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[2]^3\right )\right )} \, dK[2]+2^{2/3} \sqrt [3]{a} x \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {a x^3}{54}\right ) \int _1^x \frac {2102100 \sqrt [3]{2} b \left (-7 a \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^3+4 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^3-35 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right )\right )}{\sqrt [3]{a} \left (-10192 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^9+6370 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^9+7840 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^9-2800 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^9-3850 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{54} a K[3]^3\right ) K[3]^9+2200 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{54} a K[3]^3\right ) K[3]^9-560560 a^2 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^6+700700 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[3]^3\right ) K[3]^6-200200 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[3]^3\right ) K[3]^6-89180 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^6+78400 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^6-19250 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{54} a K[3]^3\right ) K[3]^6+7357350 a \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^3-16816800 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{54} a K[3]^3\right ) K[3]^3+7882875 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{54} a K[3]^3\right ) K[3]^3-24524500 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{54} a K[3]^3\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{54} a K[3]^3\right )\right )} \, dK[3]\right )\right \}\right \}\] ✓ Maple : cpu = 0.412 (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\, \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}})}+ \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 ) a{x}^{3} \right ) a{x}^{3} \right ) {\mbox {$_0$F$_2$}(\ ;\,5/6,7/6;\,-{\frac {a{x}^{3}}{54}})}+2200\, \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{x}^{3}{\mbox {$_0$F$_2$}(\ ;\,2/3,5/6;\,-{\frac {a{x}^{3}}{54}})} \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 ) a{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\, \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}})}+{\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})} \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 ) a{x}^{3} \right ) a{x}^{3} \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}[phone]\,{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\, \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 ) a{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\, \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 ) a{x}^{3} \right ) {\mbox {$_0$F$_2$}(\ ;\,7/6,4/3;\,-{\frac {a{x}^{3}}{54}})}+ \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}})}a{x}^{3} \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 \} \]