2.1502   ODE No. 1502

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

\[ -\left (2 x^3-6\right ) y'(x)-\left (x^4-6 x\right ) y''(x)+x^2 y^{(3)}(x)+2 x^2 y(x)=0 \] Mathematica : cpu = 0.07058 (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 = 0.684 (sec), leaf count = 104

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