4.213   ODE No. 1213

\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( {x}^{3}+1 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.072009 (sec), leaf count = 54 \[ \left \{\left \{y(x)\to \frac {\sqrt [3]{3} c_1 \, _1F_1\left (-\frac {1}{3};\frac {1}{3};-\frac {x^3}{3}\right )}{x}+\frac {c_2 x \, _1F_1\left (\frac {1}{3};\frac {5}{3};-\frac {x^3}{3}\right )}{\sqrt [3]{3}}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {{x}^{3}}{6 }}}}{x}^{{\frac {3}{2}}} \left ( {{\sl I}_{{\frac {5}{6}}}\left ({\frac {{x}^{3}}{6}}\right )}+{{\sl I}_{-{\frac {1}{6}}}\left ({\frac {{x}^{3} }{6}}\right )} \right ) +{\it \_C2}\,{{\rm e}^{-{\frac {{x}^{3}}{6}}}}{x }^{{\frac {3}{2}}} \left ( {{\sl K}_{{\frac {1}{6}}}\left ({\frac {{x}^{ 3}}{6}}\right )}-{{\sl K}_{{\frac {5}{6}}}\left ({\frac {{x}^{3}}{6}} \right )} \right ) \right \} \]