\[ a y^{(n-1)}(x)-f(x)+y^{(n)}(x)=0 \] ✓ Mathematica : cpu = 95.2137 (sec), leaf count = 120
\[\left \{\left \{y(x)\to (\text {Integrate$\grave { }\$\$$a$\$$133499}-1) (\text {Integrate$\grave { }\$\$$a$\$$133502}-1) \left (\frac {x^2}{2}-x\right ) e^{-a \text {Integrate$\grave { }\$\$$a$\$$180050}} \left (\text {Integrate}\left [e^{a K[1]} f(K[1]),\{K[1],1,\text {Integrate$\grave { }\$\$$a$\$$180050}\},\text {Assumptions}\to (\text {Integrate$\grave { }\$\$$a$\$$133499}\notin \mathbb {R}\lor (1<\Re (\text {Integrate$\grave { }\$\$$a$\$$133502})<\text {Integrate$\grave { }\$\$$a$\$$133499}\land \Im (\text {Integrate$\grave { }\$\$$a$\$$133502})=0)\lor (\Re (\text {Integrate$\grave { }\$\$$a$\$$133499})<\text {Integrate$\grave { }\$\$$a$\$$133502}<1\land \Im (\text {Integrate$\grave { }\$\$$a$\$$133499})=0))\land (\Im (x)\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$133499}<x\lor x<\text {Integrate$\grave { }\$\$$a$\$$133499}<1)\land (\Im (\text {Integrate$\grave { }\$\$$a$\$$133502})\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$180050}<\text {Integrate$\grave { }\$\$$a$\$$133502}\lor \text {Integrate$\grave { }\$\$$a$\$$133502}<\text {Integrate$\grave { }\$\$$a$\$$180050}<1)\right ]+c_1\right )+c_5 x^3+c_4 x^2+c_3 x+c_2\right \}\right \}\]
✓ Maple : cpu = 0.03 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{-ax}}{\it \_C1}}{{a}^{4}}}+{\frac {f{x}^{4}}{24\,a}}+{\frac {{x}^{3}{\it \_C2}}{6}}+{\frac {{\it \_C3}\,{x}^{2}}{2}}+{\it \_C4}\,x+{\it \_C5} \right \} \]