ODE
\[ y'''(x)-3 y''(x)+3 y'(x)-y(x)=x \left (1-e^x x^2\right ) \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.228702 (sec), leaf count = 42
\[\left \{\left \{y(x)\to -\frac {1}{120} e^x x^6+c_3 e^x x^2+x \left (-1+c_2 e^x\right )+c_1 e^x-3\right \}\right \}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 32
\[\left [y \left (x \right ) = -\frac {x^{6} {\mathrm e}^{x}}{120}-x -3+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} x \,{\mathrm e}^{x}+\textit {\_C3} \,x^{2} {\mathrm e}^{x}\right ]\] Mathematica raw input
DSolve[-y[x] + 3*y'[x] - 3*y''[x] + y'''[x] == x*(1 - E^x*x^2),y[x],x]
Mathematica raw output
{{y[x] -> -3 - (E^x*x^6)/120 + E^x*C[1] + x*(-1 + E^x*C[2]) + E^x*x^2*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+3*diff(y(x),x)-y(x) = x*(1-x^2*exp(x)), y(x))
Maple raw output
[y(x) = -1/120*x^6*exp(x)-x-3+_C1*exp(x)+_C2*x*exp(x)+_C3*x^2*exp(x)]