\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) ={\frac { \left ( 7\,a{x}^{2}+5 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( a{x}^{2}+1 \right ) }}-{\frac { \left ( 15\,a{x}^{2}+5 \right ) y \left ( x \right ) }{{x}^{2} \left ( a{x}^{2}+1 \right ) }}=0} \]
Mathematica: cpu = 0.057507 (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 = 0.032 (sec), leaf count = 20 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{5}+{\it \_C2}\, \left ( 2 \,a{x}^{3}+x \right ) \right \} \]