\[ y''(x)=\frac {\left (2 x^2+1\right ) y'(x)}{x^3}-\frac {\left (a x^4+10 x^2+1\right ) y(x)}{4 x^6} \] ✓ Mathematica : cpu = 0.0478268 (sec), leaf count = 77
DSolve[Derivative[2][y][x] == -1/4*((1 + 10*x^2 + a*x^4)*y[x])/x^6 + ((1 + 2*x^2)*Derivative[1][y][x])/x^3,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{-\frac {1}{4 x^2}} x^{\frac {3}{2}-\frac {\sqrt {9-a}}{2}}+\frac {c_2 e^{-\frac {1}{4 x^2}} x^{\frac {\sqrt {9-a}}{2}+\frac {3}{2}}}{\sqrt {9-a}}\right \}\right \}\] ✓ Maple : cpu = 0.065 (sec), leaf count = 42
dsolve(diff(diff(y(x),x),x) = (2*x^2+1)/x^3*diff(y(x),x)-1/4*(a*x^4+10*x^2+1)/x^6*y(x),y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {1}{4 x^{2}}} \left (x^{\frac {3}{2}-\frac {\sqrt {-a +9}}{2}} c_{2}+x^{\frac {3}{2}+\frac {\sqrt {-a +9}}{2}} c_{1}\right )\]