ODE
\[ y'''(x)+a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.157576 (sec), leaf count = 23
\[\left \{\left \{y(x)\to e^{a x} (x (c_3 x+c_2)+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 27
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{a x}+\textit {\_C2} \,{\mathrm e}^{a x} x +\textit {\_C3} \,{\mathrm e}^{a x} x^{2}]\] Mathematica raw input
DSolve[-(a^3*y[x]) + 3*a^2*y'[x] - 3*a*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(a*x)*(C[1] + x*(C[2] + x*C[3]))}}
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) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(a*x)+_C2*exp(a*x)*x+_C3*exp(a*x)*x^2]