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 = 0.0117832 (sec), leaf count = 23
\[\left \{\left \{y(x)\to e^{a x} \left (x \left (c_3 x+c_2\right )+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={{\rm e}^{ax}} \left ( {\it \_C3}\,{x}^{2}+{\it \_C2}\,x+{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(a*x)*(_C3*x^2+_C2*x+_C1)