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 = 0.0876336 (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 = 0.234 (sec), leaf count = 53

\[\left \{y \left (x \right ) = \left (c_{1} \BesselI \left (-\frac {1}{6}, \frac {x^{3}}{6}\right )+c_{1} \BesselI \left (\frac {5}{6}, \frac {x^{3}}{6}\right )-c_{2} \left (\BesselK \left (\frac {1}{6}, \frac {x^{3}}{6}\right )-\BesselK \left (\frac {5}{6}, \frac {x^{3}}{6}\right )\right )\right ) x^{\frac {3}{2}} {\mathrm e}^{-\frac {x^{3}}{6}}\right \}\]