2.1491   ODE No. 1491

\[ \left (-4 a^2 \nu ^2+4 a^2 x^{2 a}+1\right ) y'(x)+x^2 y^{(3)}(x)+3 x y''(x)=4 a^3 x^{2 a-1} y(x) \] Mathematica : cpu = 0.0315956 (sec), leaf count = 102


\[\left \{\left \{y(x)\to c_2 \left (x^{2 a}\right )^{-\nu } \, _1F_2\left (-\nu -\frac {1}{2};1-2 \nu ,1-\nu ;-x^{2 a}\right )+c_3 \left (x^{2 a}\right )^{\nu } \, _1F_2\left (\nu -\frac {1}{2};\nu +1,2 \nu +1;-x^{2 a}\right )+c_1 \, _1F_2\left (-\frac {1}{2};1-\nu ,\nu +1;-x^{2 a}\right )\right \}\right \}\] Maple : cpu = 0.076 (sec), leaf count = 88


\[y \relax (x ) = c_{1} \hypergeom \left (\left [-\frac {1}{2}\right ], \left [-\nu +1, \nu +1\right ], -x^{2 a}\right )+c_{2} x^{-2 a \nu } \hypergeom \left (\left [-\frac {1}{2}-\nu \right ], \left [1-2 \nu , -\nu +1\right ], -x^{2 a}\right )+c_{3} x^{2 a \nu } \hypergeom \left (\left [\nu -\frac {1}{2}\right ], \left [\nu +1, 2 \nu +1\right ], -x^{2 a}\right )\]