\[ y''(x)=-\frac {b y(x)}{x^2 \left (a+x^2\right )}-\frac {\left (a+2 x^2\right ) y'(x)}{x \left (a+x^2\right )} \] ✓ Mathematica : cpu = 0.101726 (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 = 0.048 (sec), leaf count = 73
\[ \left \{ y \left ( x \right ) ={1 \left ( {\it \_C2}\, \left ( \left ( {\frac {1}{x} \left ( 2\,a+2\,\sqrt {a}\sqrt {{x}^{2}+a} \right ) } \right ) ^{{i\sqrt {b}{\frac {1}{\sqrt {a}}}}} \right ) ^{2}+{\it \_C1} \right ) \left ( \left ( {\frac {1}{x} \left ( 2\,a+2\,\sqrt {a}\sqrt {{x}^{2}+a} \right ) } \right ) ^{{i\sqrt {b}{\frac {1}{\sqrt {a}}}}} \right ) ^{-1}} \right \} \]