ODE
\[ y'''(x)-3 y''(x)-y'(x)+3 y(x)=x^2 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0121764 (sec), leaf count = 42
\[\left \{\left \{y(x)\to c_1 e^{-x}+c_2 e^x+c_3 e^{3 x}+\frac {1}{27} \left (9 x^2+6 x+20\right )\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}}{3}}+{\frac {2\,x}{9}}+{\frac {20}{27}}+{\it \_C1}\,{{\rm e}^{x}}+{{\rm e}^{-x}}{\it \_C2}+{\it \_C3}\,{{\rm e}^{3\,x}} \right \} \] Mathematica raw input
DSolve[3*y[x] - y'[x] - 3*y''[x] + y'''[x] == x^2,y[x],x]
Mathematica raw output
{{y[x] -> (20 + 6*x + 9*x^2)/27 + C[1]/E^x + E^x*C[2] + E^(3*x)*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)-diff(y(x),x)+3*y(x) = x^2, y(x),'implicit')
Maple raw output
y(x) = 1/3*x^2+2/9*x+20/27+_C1*exp(x)+exp(-x)*_C2+_C3*exp(3*x)