2.1213   ODE No. 1213

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

\[ \left (x^3+1\right ) x y'(x)+x^2 y''(x)-y(x)=0 \] Mathematica : cpu = 0.0836695 (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 = 0.168 (sec), leaf count = 53

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