\[ \left (-4 a^2 \nu ^2+4 a^2 x^{2 a}+1\right ) y'(x)+x^2 y^{(3)}(x)+3 x y''(x)=4 a^3 x^{2 a-1} y(x) \] ✓ Mathematica : cpu = 0.03516 (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 = 0.099 (sec), leaf count = 88
\[\left \{y \left (x \right ) = c_{2} x^{-2 a \nu } \hypergeom \left (\left [-\nu -\frac {1}{2}\right ], \left [-2 \nu +1, -\nu +1\right ], -x^{2 a}\right )+c_{3} x^{2 a \nu } \hypergeom \left (\left [\nu -\frac {1}{2}\right ], \left [\nu +1, 2 \nu +1\right ], -x^{2 a}\right )+c_{1} \hypergeom \left (\left [-\frac {1}{2}\right ], \left [\nu +1, -\nu +1\right ], -x^{2 a}\right )\right \}\]