\[ y''(x)=-\frac {y(x) \left (A x^2+B\right )}{x \left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )}-\frac {y'(x) \left (x^2 \left (\left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right )+\left (x^2-\text {a1}\right ) \left (x^2-\text {a3}\right )+\left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )\right )+\left (\text {a1}-x^2\right ) \left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )\right )}{x \left (x^2-\text {a1}\right ) \left (x^2-\text {a2}\right ) \left (x^2-\text {a3}\right )} \] ✗ Mathematica : cpu = 28.9764 (sec), leaf count = 0
DSolve[Derivative[2][y][x] == -(((B + A*x^2)*y[x])/(x*(-a1 + x^2)*(-a2 + x^2)*(-a3 + x^2))) - (((a1 - x^2)*(-a2 + x^2)*(-a3 + x^2) + x^2*((-a1 + x^2)*(-a2 + x^2) + (-a1 + x^2)*(-a3 + x^2) + (-a2 + x^2)*(-a3 + x^2)))*Derivative[1][y][x])/(x*(-a1 + x^2)*(-a2 + x^2)*(-a3 + x^2)),y[x],x]
, DifferentialRoot result
\[\left \{\left \{y(x)\to (x)\right \}\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(diff(diff(y(x),x),x) = -(x^2*((x^2-a1)*(x^2-a2)+(x^2-a2)*(x^2-a3)+(x^2-a3)*(x^2-a1))-(x^2-a1)*(x^2-a2)*(x^2-a3))/x/(x^2-a1)/(x^2-a2)/(x^2-a3)*diff(y(x),x)-(A*x^2+B)/x/(x^2-a1)/(x^2-a2)/(x^2-a3)*y(x),y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \operatorname {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )+\frac {\left (x^{2} \left (\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right )+\left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )+\left (x^{2}-\operatorname {a3} \right ) \left (x^{2}-\operatorname {a1} \right )\right )-\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )\right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}+\frac {\left (A \,x^{2}+B \right ) \textit {\_Y} \left (x \right )}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]