\[ y''(x)=-\frac {y(x) \left (A x^2+B\right )}{x \left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )}-\frac {y'(x) \left (x^2 \left (\left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right )+\left (x^2-\text {a1}\right ) \left (x^2-\text {a3}\right )+\left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )\right )-\left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )\right )}{x \left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )} \] ✗ Mathematica : cpu = 75.4823 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\left (A \unicode {f817}^2+B\right ) \unicode {f818}(\unicode {f817})+\left (2 \unicode {f817}^6-\text {a1} \unicode {f817}^4-\text {a2} \unicode {f817}^4-\text {a3} \unicode {f817}^4+\text {a1} \text {a2} \text {a3}\right ) \unicode {f818}'(\unicode {f817})-\unicode {f817} \left (\text {a1}-\unicode {f817}^2\right ) \left (\text {a2}-\unicode {f817}^2\right ) \left (\text {a3}-\unicode {f817}^2\right ) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2\right \}\right )(x)\right \}\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +{\frac { \left ( {x}^{2} \left ( \left ( {x}^{2}-{\it a1} \right ) \left ( {x}^{2}-{\it a2} \right ) + \left ( {x}^{2}-{\it a2} \right ) \left ( {x}^{2}-{\it a3} \right ) + \left ( {x}^{2}-{\it a3} \right ) \left ( {x}^{2}-{\it a1} \right ) \right ) - \left ( {x}^{2}-{\it a1} \right ) \left ( {x}^{2}-{\it a2} \right ) \left ( {x}^{2}-{\it a3} \right ) \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{ \left ( {x}^{2}-{\it a1} \right ) \left ( {x}^{2}-{\it a2} \right ) x \left ( {x}^{2}-{\it a3} \right ) }}+{\frac { \left ( A{x}^{2}+B \right ) {\it \_Y} \left ( x \right ) }{ \left ( {x}^{2}-{\it a1} \right ) \left ( {x}^{2}-{\it a2} \right ) x \left ( {x}^{2}-{\it a3} \right ) }} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]