2.1502   ODE No. 1502

\[ -\left (x^4-6 x\right ) y''(x)-\left (2 x^3-6\right ) y'(x)+x^2 y^{(3)}(x)+2 x^2 y(x)=0 \] Mathematica : cpu = 0.0709371 (sec), leaf count = 98


\[\left \{\left \{y(x)\to \frac {c_2 \Gamma \left (\frac {1}{3}\right ) \, _2F_2\left (-\frac {2}{3},\frac {1}{3};\frac {2}{3},\frac {4}{3};\frac {x^3}{3}\right )}{3 x \Gamma \left (\frac {4}{3}\right )}+\frac {\sqrt [3]{-\frac {1}{3}} c_3 \Gamma \left (\frac {2}{3}\right ) \, _2F_2\left (-\frac {1}{3},\frac {2}{3};\frac {4}{3},\frac {5}{3};\frac {x^3}{3}\right )}{3 \Gamma \left (\frac {5}{3}\right )}+\frac {c_1}{x^2}\right \}\right \}\] Maple : cpu = 0.366 (sec), leaf count = 104


\[y \relax (x ) = \frac {c_{3} \left (\int -{\mathrm e}^{\frac {x^{3}}{6}} \sqrt {x}\, \left (-\BesselK \left (\frac {5}{6}, -\frac {x^{3}}{6}\right ) x^{3}+\BesselK \left (\frac {1}{6}, -\frac {x^{3}}{6}\right ) x^{3}-2 \BesselK \left (\frac {1}{6}, -\frac {x^{3}}{6}\right )\right )d x \right )+c_{2} \left (\int {\mathrm e}^{\frac {x^{3}}{6}} \sqrt {x}\, \left (\BesselI \left (\frac {1}{6}, -\frac {x^{3}}{6}\right ) x^{3}+\BesselI \left (-\frac {5}{6}, -\frac {x^{3}}{6}\right ) x^{3}-2 \BesselI \left (\frac {1}{6}, -\frac {x^{3}}{6}\right )\right )d x \right )+c_{1}}{x^{2}}\]