\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( 2\,{x}^{2}+a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( {x}^{2}+a \right ) }}-{\frac {by \left ( x \right ) }{{x}^{2} \left ( {x}^{2}+a \right ) }}=0} \]
Mathematica: cpu = 0.096512 (sec), leaf count = 82 \[ \left \{\left \{y(x)\to c_2 \sin \left (\frac {\sqrt {b} \left (\log (x)-\log \left (\sqrt {a} \sqrt {a+x^2}+a\right )\right )}{\sqrt {a}}\right )+c_1 \cos \left (\frac {\sqrt {b} \left (\log (x)-\log \left (\sqrt {a} \sqrt {a+x^2}+a\right )\right )}{\sqrt {a}}\right )\right \}\right \} \]
Maple: cpu = 0.016 (sec), leaf count = 71 \[ \left \{ y \left ( x \right ) ={{\it \_C1} \left ( \left ( {\frac {1}{x} \left ( 2\,a+2\,\sqrt {a}\sqrt {{x}^{2}+a} \right ) } \right ) ^{{i \sqrt {b}{\frac {1}{\sqrt {a}}}}} \right ) ^{-1}}+{\it \_C2}\, \left ( { \frac {1}{x} \left ( 2\,a+2\,\sqrt {a}\sqrt {{x}^{2}+a} \right ) } \right ) ^{{i\sqrt {b}{\frac {1}{\sqrt {a}}}}} \right \} \]