\[ a x y(x)-b+2 x y^{(3)}(x)+3 y''(x)=0 \] ✓ Mathematica : cpu = 6.62774 (sec), leaf count = 3629
DSolve[-b + a*x*y[x] + 3*Derivative[2][y][x] + 2*x*Derivative[3][y][x] == 0,y[x],x]
\[\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 = 0.286 (sec), leaf count = 1616
dsolve(2*x*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+a*x*y(x)-b=0,y(x))
\[\text {Expression too large to display}\]