\[ a y^{(4)}(x)-f(x)+y^{(5)}(x)=0 \] ✓ Mathematica : cpu = 459.877 (sec), leaf count = 117
\[\left \{\left \{y(x)\to (\text {Integrate$\grave { }\$\$$a$\$$15130244}-1) (\text {Integrate$\grave { }\$\$$a$\$$15260410}-1) (\text {Integrate$\grave { }\$\$$a$\$$15292862}-1) (x-1) e^{-a \text {Integrate$\grave { }\$\$$a$\$$15298906}} \left (\text {Integrate}\left [e^{a K[1]} f(K[1]),\{K[1],1,\text {Integrate$\grave { }\$\$$a$\$$15298906}\},\text {Assumptions}\to (\Im (\text {Integrate$\grave { }\$\$$a$\$$15130244})\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$15260410}<\text {Integrate$\grave { }\$\$$a$\$$15130244}\lor \text {Integrate$\grave { }\$\$$a$\$$15130244}<\text {Integrate$\grave { }\$\$$a$\$$15260410}<1)\land (\Im (\text {Integrate$\grave { }\$\$$a$\$$15260410})\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$15292862}<\text {Integrate$\grave { }\$\$$a$\$$15260410}\lor \text {Integrate$\grave { }\$\$$a$\$$15260410}<\text {Integrate$\grave { }\$\$$a$\$$15292862}<1)\land (\Im (\text {Integrate$\grave { }\$\$$a$\$$15292862})\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$15298906}<\text {Integrate$\grave { }\$\$$a$\$$15292862}\lor \text {Integrate$\grave { }\$\$$a$\$$15292862}<\text {Integrate$\grave { }\$\$$a$\$$15298906}<1)\land (\Im (x)\neq 0\lor 1<\text {Integrate$\grave { }\$\$$a$\$$15130244}<x\lor x<\text {Integrate$\grave { }\$\$$a$\$$15130244}<1)\right ]+c_1\right )+c_5 x^3+c_4 x^2+c_3 x+c_2\right \}\right \}\] ✓ Maple : cpu = 0.04 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C3}\,{x}^{2}}{2}}+{\frac {{\it \_C2}\,{x}^{3}}{6}}+{\frac {{{\rm e}^{-ax}}{\it \_C1}}{{a}^{4}}}+{\frac {f{x}^{4}}{24\,a}}+{\it \_C4}\,x+{\it \_C5} \right \} \]