2.1524   ODE No. 1524

\[ x^6 y^{(3)}(x)+x^2 y''(x)-2 y(x)=0 \] Mathematica : cpu = 0.156564 (sec), leaf count = 96


\[\left \{\left \{y(x)\to -\frac {\left (-\frac {1}{3}\right )^{2/3} c_2 x \Gamma \left (\frac {1}{3}\right ) \, _2F_2\left (-\frac {2}{3},\frac {1}{3};\frac {2}{3},\frac {4}{3};\frac {1}{3 x^3}\right )}{3 \Gamma \left (\frac {4}{3}\right )}+\frac {c_3 \Gamma \left (\frac {2}{3}\right ) \, _2F_2\left (-\frac {1}{3},\frac {2}{3};\frac {4}{3},\frac {5}{3};\frac {1}{3 x^3}\right )}{9 \Gamma \left (\frac {5}{3}\right )}+c_1 x^2\right \}\right \}\] Maple : cpu = 0.408 (sec), leaf count = 98


\[y \relax (x ) = x^{2} \left (\left (\int \frac {{\mathrm e}^{\frac {1}{6 x^{3}}} \left (2 x^{3} \BesselI \left (\frac {1}{6}, -\frac {1}{6 x^{3}}\right )-\BesselI \left (\frac {1}{6}, -\frac {1}{6 x^{3}}\right )-\BesselI \left (-\frac {5}{6}, -\frac {1}{6 x^{3}}\right )\right )}{x^{\frac {11}{2}}}d x \right ) c_{3}+\left (\int \frac {{\mathrm e}^{\frac {1}{6 x^{3}}} \left (2 x^{3} \BesselK \left (\frac {1}{6}, -\frac {1}{6 x^{3}}\right )+\BesselK \left (\frac {5}{6}, -\frac {1}{6 x^{3}}\right )-\BesselK \left (\frac {1}{6}, -\frac {1}{6 x^{3}}\right )\right )}{x^{\frac {11}{2}}}d x \right ) c_{2}+c_{1}\right )\]