\[ a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)-e^{a x}+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0081311 (sec), leaf count = 46
DSolve[-E^(a*x) - a^3*y[x] + 3*a^2*Derivative[1][y][x] - 3*a*Derivative[2][y][x] + Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{6} x^3 e^{a x}+c_3 x^2 e^{a x}+c_2 x e^{a x}+c_1 e^{a x}\right \}\right \}\] ✓ Maple : cpu = 0.025 (sec), leaf count = 27
dsolve(diff(diff(diff(y(x),x),x),x)-3*a*diff(diff(y(x),x),x)+3*a^2*diff(y(x),x)-a^3*y(x)-exp(a*x)=0,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{a x} \left (x^{3}+6 x^{2} c_{3}+6 x c_{2}+6 c_{1}\right )}{6}\]