ODE
\[ y'''(x)+2 y''(x)+y'(x)=(x-1) x \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0311906 (sec), leaf count = 41
\[\left \{\left \{y(x)\to -e^{-x} \left (c_2 (x+1)+c_1\right )+c_3+\frac {x^3}{3}-\frac {5 x^2}{2}+8 x\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) ={\frac { \left ( -6\,{\it \_C1}\,x-6\,{\it \_C1}-6\,{\it \_C2} \right ) {{\rm e}^{-x}}}{6}}+{\frac {{x}^{3}}{3}}-{\frac {5\,{x}^{2}}{2}}+8\,x+{\it \_C3} \right \} \] Mathematica raw input
DSolve[y'[x] + 2*y''[x] + y'''[x] == (-1 + x)*x,y[x],x]
Mathematica raw output
{{y[x] -> 8*x - (5*x^2)/2 + x^3/3 - (C[1] + (1 + x)*C[2])/E^x + C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x)+diff(y(x),x) = x*(x-1), y(x),'implicit')
Maple raw output
y(x) = 1/6*(-6*_C1*x-6*_C1-6*_C2)*exp(-x)+1/3*x^3-5/2*x^2+8*x+_C3