ODE
\[ y'''(x)+2 y''(x)+y'(x)=(x-1) x \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.210315 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {1}{6} x \left (2 x^2-15 x+48\right )-e^{-x} (c_2 (x+1)+c_1)+c_3\right \}\right \}\]
Maple ✓
cpu = 0.228 (sec), leaf count = 42
\[\left [y \left (x \right ) = \frac {x^{3}}{3}-\textit {\_C2} \,{\mathrm e}^{-x}+\textit {\_C1} \left (-x \,{\mathrm e}^{-x}-{\mathrm e}^{-x}\right )-\frac {5 x^{2}}{2}+8 x +\textit {\_C3}\right ]\] Mathematica raw input
DSolve[y'[x] + 2*y''[x] + y'''[x] == (-1 + x)*x,y[x],x]
Mathematica raw output
{{y[x] -> (x*(48 - 15*x + 2*x^2))/6 - (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))
Maple raw output
[y(x) = 1/3*x^3-_C2*exp(-x)+_C1*(-x*exp(-x)-exp(-x))-5/2*x^2+8*x+_C3]