\[ y''(x)=-\frac {y(x) \left (A x^2+B\right )}{x \left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )}-\frac {y'(x) \left (x^2 \left (\left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right )+\left (x^2-\text {a1}\right ) \left (x^2-\text {a3}\right )+\left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )\right )+\left (\text {a1}-x^2\right ) \left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )\right )}{x \left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )} \] ✗ Mathematica : cpu = 50.8363 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to (x)\right \}\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[\left \{y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )+\frac {\left (A \,x^{2}+B \right ) \textit {\_Y} \left (x \right )}{\left (x^{2}-\mathit {a1} \right ) \left (x^{2}-\mathit {a2} \right ) \left (x^{2}-\mathit {a3} \right ) x}+\frac {\left (\left (\left (x^{2}-\mathit {a1} \right ) \left (x^{2}-\mathit {a2} \right )+\left (x^{2}-\mathit {a2} \right ) \left (x^{2}-\mathit {a3} \right )+\left (x^{2}-\mathit {a3} \right ) \left (x^{2}-\mathit {a1} \right )\right ) x^{2}-\left (x^{2}-\mathit {a1} \right ) \left (x^{2}-\mathit {a2} \right ) \left (x^{2}-\mathit {a3} \right )\right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )}{\left (x^{2}-\mathit {a1} \right ) \left (x^{2}-\mathit {a2} \right ) \left (x^{2}-\mathit {a3} \right ) x}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right \}\]