2.1532   ODE No. 1532

\[ n y(x)+y^{(3)}(x)+x y'(x)=0 \] Mathematica : cpu = 0.0118426 (sec), leaf count = 103


\[\left \{\left \{y(x)\to \frac {c_2 x \, _1F_2\left (\frac {n}{3}+\frac {1}{3};\frac {2}{3},\frac {4}{3};-\frac {x^3}{9}\right )}{3^{2/3}}+c_1 \, _1F_2\left (\frac {n}{3};\frac {1}{3},\frac {2}{3};-\frac {x^3}{9}\right )+\frac {c_3 x^2 \, _1F_2\left (\frac {n}{3}+\frac {2}{3};\frac {4}{3},\frac {5}{3};-\frac {x^3}{9}\right )}{3 \sqrt [3]{3}}\right \}\right \}\] Maple : cpu = 0.083 (sec), leaf count = 58


\[y \relax (x ) = c_{1} \hypergeom \left (\left [\frac {n}{3}\right ], \left [\frac {1}{3}, \frac {2}{3}\right ], -\frac {x^{3}}{9}\right )+c_{2} x \hypergeom \left (\left [\frac {1}{3}+\frac {n}{3}\right ], \left [\frac {2}{3}, \frac {4}{3}\right ], -\frac {x^{3}}{9}\right )+c_{3} x^{2} \hypergeom \left (\left [\frac {2}{3}+\frac {n}{3}\right ], \left [\frac {4}{3}, \frac {5}{3}\right ], -\frac {x^{3}}{9}\right )\]