\[ \left (-4 a^2 \nu ^2+4 a^2 x^{2 a}+1\right ) y'(x)+x^2 y^{(3)}(x)+3 x y''(x)=4 a^3 x^{2 a-1} y(x) \] ✓ Mathematica : cpu = 0.0321792 (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 = 0.258 (sec), leaf count = 88
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_1$F$_2$}(-{\frac {1}{2}};\,\nu +1,-\nu +1;\,-{x}^{2\,a})}+{\it \_C2}\,{x}^{-2\,a\nu }{\mbox {$_1$F$_2$}(-{\frac {1}{2}}-\nu ;\,1-2\,\nu ,-\nu +1;\,-{x}^{2\,a})}+{\it \_C3}\,{x}^{2\,a\nu }{\mbox {$_1$F$_2$}(\nu -{\frac {1}{2}};\,\nu +1,2\,\nu +1;\,-{x}^{2\,a})} \right \} \]