5.76   ODE No. 1524

\[ \boxed { {x}^{6}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\,y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.143518 (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 = 0.390 (sec), leaf count = 104 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}+{\it \_C2}\,\int \!{1 {{\rm e}^{{\frac {1}{6\,{x}^{3}}}}} \left ( 2\,{x}^{3}{{\sl I}_{1/6 }\left (-1/6\,{x}^{-3}\right )}-{{\sl I}_{{\frac {1}{6}}}\left (-{\frac { 1}{6\,{x}^{3}}}\right )}-{{\sl I}_{-{\frac {5}{6}}}\left (-{\frac {1}{6 \,{x}^{3}}}\right )} \right ) {x}^{-{\frac {11}{2}}}}\,{\rm d}x{x}^{2}+{ \it \_C3}\,\int \!{1{{\rm e}^{{\frac {1}{6\,{x}^{3}}}}} \left ( 2\,{x}^ {3}{{\sl K}_{1/6}\left (-1/6\,{x}^{-3}\right )}+{{\sl K}_{{\frac {5}{6}} }\left (-{\frac {1}{6\,{x}^{3}}}\right )}-{{\sl K}_{{\frac {1}{6}} }\left (-{\frac {1}{6\,{x}^{3}}}\right )} \right ) {x}^{-{\frac {11}{2}}} }\,{\rm d}x{x}^{2} \right \} \]