\[ y''(x)=\frac {\left (7 a x^2+5\right ) y'(x)}{x \left (a x^2+1\right )}-\frac {\left (15 a x^2+5\right ) y(x)}{x^2 \left (a x^2+1\right )} \] ✓ Mathematica : cpu = 0.0382677 (sec), leaf count = 27
\[\left \{\left \{y(x)\to c_1 x^5-\frac {1}{4} c_2 x \left (2 a x^2+1\right )\right \}\right \}\] ✓ Maple : cpu = 0.024 (sec), leaf count = 20
\[y \relax (x ) = x^{5} c_{1}+2 a \,x^{3} c_{2}+x c_{2}\]