\[ y''(x)=-\frac {\left (a+3 x^2\right ) y'(x)}{x^3}-\frac {b y(x)}{x^6} \] ✓ Mathematica : cpu = 0.0097342 (sec), leaf count = 93
DSolve[Derivative[2][y][x] == -((b*y[x])/x^6) - ((a + 3*x^2)*Derivative[1][y][x])/x^3,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{-\frac {\sqrt {b} \left (-\frac {\sqrt {a^2-4 b}}{\sqrt {b}}-\frac {a}{\sqrt {b}}\right )}{4 x^2}}+c_2 e^{-\frac {\sqrt {b} \left (\frac {\sqrt {a^2-4 b}}{\sqrt {b}}-\frac {a}{\sqrt {b}}\right )}{4 x^2}}\right \}\right \}\] ✓ Maple : cpu = 0.052 (sec), leaf count = 45
dsolve(diff(diff(y(x),x),x) = -1/x^3*(3*x^2+a)*diff(y(x),x)-b/x^6*y(x),y(x))
\[y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {-a +\sqrt {a^{2}-4 b}}{4 x^{2}}}+c_{2} {\mathrm e}^{\frac {a +\sqrt {a^{2}-4 b}}{4 x^{2}}}\]