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 = 0.16047 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {1}{6} e^{a x} \left (x^3+6 c_3 x^2+6 c_2 x+6 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 36
\[\left [y \left (x \right ) = \frac {x^{3} {\mathrm e}^{a x}}{6}+\textit {\_C1} \,{\mathrm e}^{a x}+\textit {\_C2} \,{\mathrm e}^{a x} x +\textit {\_C3} \,{\mathrm e}^{a x} x^{2}\right ]\] 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))
Maple raw output
[y(x) = 1/6*x^3*exp(a*x)+_C1*exp(a*x)+_C2*exp(a*x)*x+_C3*exp(a*x)*x^2]