\[ -y^{(4)}(x) (x (a A(5)-A(4))+A(5))-y^{(3)}(x) (x (a A(4)-A(3))+A(4))-(x (a A(3)-A(2))+A(3)) y''(x)-(x (a A(2)-A(1))+A(2)) y'(x)-x (a A(1)-A(0))-A(1)+x y^{(5)}(x)=0 \] ✗ Mathematica : cpu = 82.7583 (sec), leaf count = 0
DSolve[-A[1] - x*(-A[0] + a*A[1]) - (A[2] + x*(-A[1] + a*A[2]))*Derivative[1][y][x] - (A[3] + x*(-A[2] + a*A[3]))*Derivative[2][y][x] - (A[4] + x*(-A[3] + a*A[4]))*Derivative[3][y][x] - (A[5] + x*(-A[4] + a*A[5]))*Derivative[4][y][x] + x*Derivative[5][y][x] == 0,y[x],x]
, DifferentialRoot result
\[\left \{\left \{y(x)\to (x)\right \}\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(x*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-(a*A[1]-A[0])*x-A[1]-((a*A[2]-A[1])*x+A[2])*diff(y(x),x)-((a*A[3]-A[2])*x+A[3])*diff(diff(y(x),x),x)-((a*A[4]-A[3])*x+A[4])*diff(diff(diff(y(x),x),x),x)-((a*A[5]-A[4])*x+A[5])*diff(diff(diff(diff(y(x),x),x),x),x)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \int \mathit {DESol}\left (\left \{-\frac {\left (a x A_{2}-x A_{1}+A_{2}\right ) \textit {\_Y} \left (x \right )}{x}-\frac {\left (a x A_{3}-x A_{2}+A_{3}\right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )}{x}-\frac {\left (a x A_{4}-x A_{3}+A_{4}\right ) \left (\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right )}{x}-\frac {\left (a x A_{5}-x A_{4}+A_{5}\right ) \left (\frac {d^{3}}{d x^{3}}\textit {\_Y} \left (x \right )\right )}{x}+\frac {d^{4}}{d x^{4}}\textit {\_Y} \left (x \right )-\frac {a x A_{1}-x A_{0}+A_{1}}{x}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )d x +c_{1}\]