\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -3\,a{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +3\,{a}^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{a}^{3}y \left ( x \right ) -{{\rm e}^{ax}}=0} \]
Mathematica: cpu = 0.018002 (sec), leaf count = 46 \[ \left \{\left \{y(x)\to c_3 x^2 e^{a x}+c_2 x e^{a x}+c_1 e^{a x}+\frac {1}{6} x^3 e^{a x}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 36 \[ \left \{ y \left ( x \right ) ={\frac {{x}^{3}{{\rm e}^{ax}}}{6}}+{\it \_C1}\,{{\rm e}^{ax}}+{\it \_C2}\,{{\rm e}^{ax}}x+{\it \_C3}\,{{\rm e} ^{ax}}{x}^{2} \right \} \]