\[ -\left (4 n^2-1\right ) x^2 y''(x)+\left (4 n^2-1\right ) x y'(x)+x^4 y^{(4)}(x)-4 x^4 y(x)+4 x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.80731 (sec), leaf count = 140
\[\left \{\left \{y(x)\to c_1 \, _0F_3\left (;\frac {1}{2},1-\frac {n}{2},\frac {n}{2}+1;\frac {x^4}{64}\right )+\frac {1}{8} i c_2 x^2 \, _0F_3\left (;\frac {3}{2},\frac {3}{2}-\frac {n}{2},\frac {n}{2}+\frac {3}{2};\frac {x^4}{64}\right )+c_3 \left (\frac {i}{2}\right )^{-n} \Gamma (1-n)^2 \left (\text {ber}_{-n}(x){}^2+\text {bei}_{-n}(x){}^2\right )+c_4 \left (\frac {i}{2}\right )^n \Gamma (n+1)^2 \left (\text {ber}_n(x){}^2+\text {bei}_n(x){}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.315 (sec), leaf count = 77
\[y \relax (x ) = \left (\BesselY \left (n , \left (\frac {1}{2}-\frac {i}{2}\right ) \sqrt {2}\, x \right ) c_{3}+c_{1} \BesselJ \left (n , \left (\frac {1}{2}-\frac {i}{2}\right ) \sqrt {2}\, x \right )\right ) \BesselJ \left (n , \left (\frac {1}{2}+\frac {i}{2}\right ) \sqrt {2}\, x \right )+\BesselY \left (n , \left (\frac {1}{2}+\frac {i}{2}\right ) \sqrt {2}\, x \right ) \left (\BesselY \left (n , \left (\frac {1}{2}-\frac {i}{2}\right ) \sqrt {2}\, x \right ) c_{4}+c_{2} \BesselJ \left (n , \left (\frac {1}{2}-\frac {i}{2}\right ) \sqrt {2}\, x \right )\right )\]