\[ y''(x)=\frac {y'(x)}{x}-\frac {a y(x)}{x^6} \] ✓ Mathematica : cpu = 0.0927283 (sec), leaf count = 60
DSolve[Derivative[2][y][x] == -((a*y[x])/x^6) + Derivative[1][y][x]/x,y[x],x]
\[\left \{\left \{y(x)\to c_1 x^2 e^{\frac {i \sqrt {a}}{2 x^2}}-\frac {i c_2 x^2 e^{-\frac {i \sqrt {a}}{2 x^2}}}{2 \sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.045 (sec), leaf count = 35
dsolve(diff(diff(y(x),x),x) = 1/x*diff(y(x),x)-a/x^6*y(x),y(x))
\[y \left (x \right ) = x^{2} \left (\cosh \left (\frac {\sqrt {-a}}{2 x^{2}}\right ) c_{2}+\sinh \left (\frac {\sqrt {-a}}{2 x^{2}}\right ) c_{1}\right )\]