\[ a^4 \left (-x^3\right ) y(x)+x^3 y^{(4)}(x)+2 x^2 y^{(3)}(x)-x y''(x)+y'(x)=0 \] ✓ Mathematica : cpu = 0.199962 (sec), leaf count = 100
DSolve[-(a^4*x^3*y[x]) + Derivative[1][y][x] - x*Derivative[2][y][x] + 2*x^2*Derivative[3][y][x] + x^3*Derivative[4][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_4 G_{0,4}^{2,0}\left (\frac {a^4 x^4}{256}|\begin {array}{c} 0,0,\frac {1}{2},\frac {1}{2} \\\end {array}\right )+c_2 G_{0,4}^{2,0}\left (\frac {a^4 x^4}{256}|\begin {array}{c} \frac {1}{2},\frac {1}{2},0,0 \\\end {array}\right )+\frac {1}{8} i c_1 (I_0(a x)-J_0(a x))+\frac {1}{2} c_3 (J_0(a x)+I_0(a x))\right \}\right \}\] ✓ Maple : cpu = 0.13 (sec), leaf count = 33
dsolve(x^3*diff(diff(diff(diff(y(x),x),x),x),x)+2*x^2*diff(diff(diff(y(x),x),x),x)-x*diff(diff(y(x),x),x)+diff(y(x),x)-a^4*x^3*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \BesselI \left (0, a x \right )+c_{2} \BesselJ \left (0, a x \right )+c_{3} \BesselK \left (0, a x \right )+c_{4} \BesselY \left (0, a x \right )\]