2.1450   ODE No. 1450

\[ a x^3 y(x)-b x+y^{(3)}(x)=0 \] Mathematica : cpu = 4.07642 (sec), leaf count = 3595


\[\left \{\left \{y(x)\to \frac {1}{6} \sqrt [3]{a} c_3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {a x^6}{216}\right ) x^2+\frac {\sqrt [6]{a} c_2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {a x^6}{216}\right ) x}{\sqrt {6}}+c_1 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {a x^6}{216}\right )+\frac {1}{6} \left (\sqrt [3]{a} \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {a x^6}{216}\right ) \int _1^x\frac {16816800 \left (-7 a b \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^7+4 a b \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^7-140 b \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) K[3]\right )}{\sqrt [3]{a} \left (-5096 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^{18}+3185 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^{18}+3920 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^{18}-1400 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^{18}-1925 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{216} a K[3]^6\right ) K[3]^{18}+1100 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{216} a K[3]^6\right ) K[3]^{18}-1121120 a^2 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^{12}+1401400 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[3]^6\right ) K[3]^{12}-400400 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[3]^6\right ) K[3]^{12}-178360 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^{12}+156800 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^{12}-38500 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{216} a K[3]^6\right ) K[3]^{12}+58858800 a \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^6-134534400 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[3]^6\right ) K[3]^6+63063000 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[3]^6\right ) K[3]^6-784784000 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[3]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[3]^6\right )\right )}dK[3] x^2+\sqrt {6} \sqrt [6]{a} \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {a x^6}{216}\right ) \int _1^x\frac {1401400 \sqrt {6} b \left (-14 a \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^8+5 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[2]^6\right ) K[2]^8-560 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right ) K[2]^2\right )}{\sqrt [6]{a} \left (5096 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^{18}-3185 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^{18}-3920 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^{18}+1400 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^{18}+1925 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{216} a K[2]^6\right ) K[2]^{18}-1100 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{216} a K[2]^6\right ) K[2]^{18}+1121120 a^2 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^{12}-1401400 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[2]^6\right ) K[2]^{12}+400400 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[2]^6\right ) K[2]^{12}+178360 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^{12}-156800 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^{12}+38500 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{216} a K[2]^6\right ) K[2]^{12}-58858800 a \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^6+134534400 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[2]^6\right ) K[2]^6-63063000 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[2]^6\right ) K[2]^6+784784000 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[2]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[2]^6\right )\right )}dK[2] x+6 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {a x^6}{216}\right ) \int _1^x\frac {1401400 \left (-8 a b \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^9+5 a b \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[1]^6\right ) K[1]^9-280 b \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right ) K[1]^3\right )}{-5096 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^{18}+3185 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^{18}+3920 a^3 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^{18}-1400 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^{18}-1925 a^3 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{216} a K[1]^6\right ) K[1]^{18}+1100 a^3 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{216} a K[1]^6\right ) K[1]^{18}-1121120 a^2 \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^{12}+1401400 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[1]^6\right ) K[1]^{12}-400400 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[1]^6\right ) K[1]^{12}-178360 a^2 \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {8}{3},\frac {17}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^{12}+156800 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {17}{6},\frac {19}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^{12}-38500 a^2 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {19}{6},\frac {10}{3};-\frac {1}{216} a K[1]^6\right ) K[1]^{12}+58858800 a \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {5}{3},\frac {11}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^6-134534400 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {11}{6},\frac {13}{6};-\frac {1}{216} a K[1]^6\right ) K[1]^6+63063000 a \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {13}{6},\frac {7}{3};-\frac {1}{216} a K[1]^6\right ) K[1]^6-784784000 \, _0F_2\left (;\frac {2}{3},\frac {5}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {5}{6},\frac {7}{6};-\frac {1}{216} a K[1]^6\right ) \, _0F_2\left (;\frac {7}{6},\frac {4}{3};-\frac {1}{216} a K[1]^6\right )}dK[1]\right )\right \}\right \}\] Maple : cpu = 0.218 (sec), leaf count = 1616


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