2.1524   ODE No. 1524

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

\[ x^2 y''(x)+x^6 y^{(3)}(x)-2 y(x)=0 \] Mathematica : cpu = 0.153207 (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 = 0.645 (sec), leaf count = 98

\[ \left \{ y \left ( x \right ) ={x}^{2} \left ( \int \!{{{\rm e}^{{\frac {1}{6\,{x}^{3}}}}} \left ( 2\,{x}^{3}{{\sl I}_{1/6}\left (-1/6\,{x}^{-3}\right )}-{{\sl I}_{{\frac {1}{6}}}\left (-{\frac {1}{6\,{x}^{3}}}\right )}-{{\sl I}_{-{\frac {5}{6}}}\left (-{\frac {1}{6\,{x}^{3}}}\right )} \right ) {x}^{-{\frac {11}{2}}}}\,{\rm d}x{\it \_C3}+\int \!{{{\rm e}^{{\frac {1}{6\,{x}^{3}}}}} \left ( 2\,{x}^{3}{{\sl K}_{1/6}\left (-1/6\,{x}^{-3}\right )}+{{\sl K}_{{\frac {5}{6}}}\left (-{\frac {1}{6\,{x}^{3}}}\right )}-{{\sl K}_{{\frac {1}{6}}}\left (-{\frac {1}{6\,{x}^{3}}}\right )} \right ) {x}^{-{\frac {11}{2}}}}\,{\rm d}x{\it \_C2}+{\it \_C1} \right ) \right \} \]