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 = 0.161316 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \frac {1}{27} \left (9 x^2+6 x+20\right )+c_1 e^{-x}+c_2 e^x+c_3 e^{3 x}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 30
\[\left [y \left (x \right ) = \frac {x^{2}}{3}+\frac {2 x}{9}+\frac {20}{27}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{-x}+\textit {\_C3} \,{\mathrm e}^{3 x}\right ]\] 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))
Maple raw output
[y(x) = 1/3*x^2+2/9*x+20/27+_C1*exp(x)+_C2*exp(-x)+_C3*exp(3*x)]