\[ -(x (a A(2)-A(1))+A(2)) y'(x)-(x (a A(3)-A(2))+A(3)) y''(x)-y^{(3)}(x) (x (a A(4)-A(3))+A(4))-y^{(4)}(x) (x (a A(5)-A(4))+A(5))-x (a A(1)-A(0))-A(1)+x y^{(5)}(x)=0 \] ✗ Mathematica : cpu = 82.7866 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f817} A(0)-\unicode {f817} a A(1)-A(1)+(\unicode {f817} A(1)-\unicode {f817} a A(2)-A(2)) \unicode {f818}'(\unicode {f817})+(\unicode {f817} A(2)-\unicode {f817} a A(3)-A(3)) \unicode {f818}''(\unicode {f817})+(\unicode {f817} A(3)-\unicode {f817} a A(4)-A(4)) \unicode {f818}^{(3)}(\unicode {f817})+(\unicode {f817} A(4)-\unicode {f817} a A(5)-A(5)) \unicode {f818}^{(4)}(\unicode {f817})+\unicode {f817} \unicode {f818}^{(5)}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3,\unicode {f818}^{(3)}(1)=c_4,\unicode {f818}^{(4)}(1)=c_5\right \}\right )(x)\right \}\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) =\int \!{\it DESol} \left ( \left \{ -{\frac { \left ( axA_{{2}}-xA_{{1}}+A_{{2}} \right ) {\it \_Y} \left ( x \right ) }{x}}-{\frac { \left ( axA_{{3}}-xA_{{2}}+A_{{3}} \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{x}}-{\frac { \left ( axA_{{4}}-xA_{{3}}+A_{{4}} \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) }{x}}-{\frac { \left ( axA_{{5}}-xA_{{4}}+A_{{5}} \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) }{x}}+{\frac {{\rm d}^{4}}{{\rm d}{x}^{4}}}{\it \_Y} \left ( x \right ) -{\frac {axA_{{1}}-xA_{{0}}+A_{{1}}}{x}} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \,{\rm d}x+{\it \_C1} \right \} \]