ODE
\[ y'''(x)+a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)=e^{a x} \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0221347 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {1}{6} e^{a x} \left (6 c_3 x^2+6 c_2 x+6 c_1+x^3\right )\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{ax}} \left ( 6\,{\it \_C3}\,{x}^{2}+{x}^{3}+6\,{\it \_C2}\,x+6\,{\it \_C1} \right ) }{6}} \right \} \] Mathematica raw input
DSolve[-(a^3*y[x]) + 3*a^2*y'[x] - 3*a*y''[x] + y'''[x] == E^(a*x),y[x],x]
Mathematica raw output
{{y[x] -> (E^(a*x)*(x^3 + 6*C[1] + 6*x*C[2] + 6*x^2*C[3]))/6}}
Maple raw input
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), y(x),'implicit')
Maple raw output
y(x) = 1/6*exp(a*x)*(6*_C3*x^2+x^3+6*_C2*x+6*_C1)