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−(x(aA(2)−A(1))+A(2))y′(x)−(x(aA(3)−A(2))+A(3))y″(x)−y(3)(x)(x(aA(4)−A(3))+A(4))−y(4)(x)(x(aA(5)−A(4))+A(5))−x(aA(1)−A(0))−A(1)+xy(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 \}\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
{y(x)=∫DESol({−(axA2−xA1+A2)_Y(x)x−(axA3−xA2+A3)ddx_Y(x)x−(axA4−xA3+A4)d2dx2_Y(x)x−(axA5−xA4+A5)d3dx3_Y(x)x+d4dx4_Y(x)−axA1−xA0+A1x},{_Y(x)})dx+_C1}
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