ODE
\[ y'''(x)+3 y''(x)+3 y'(x)+y(x)=e^{-x} \left (2-x^2\right ) \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.167329 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {1}{60} e^{-x} \left (-x^5+20 x^3+60 c_3 x^2+60 c_2 x+60 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.035 (sec), leaf count = 55
\[\left [y \left (x \right ) = \frac {x^{3} \left (x^{2}-20\right ) \left (-x^{2}+2\right ) {\mathrm e}^{-x}}{60 x^{2}-120}+{\mathrm e}^{-x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{-x} x +\textit {\_C3} \,{\mathrm e}^{-x} x^{2}\right ]\] Mathematica raw input
DSolve[y[x] + 3*y'[x] + 3*y''[x] + y'''[x] == (2 - x^2)/E^x,y[x],x]
Mathematica raw output
{{y[x] -> (20*x^3 - x^5 + 60*C[1] + 60*x*C[2] + 60*x^2*C[3])/(60*E^x)}}
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) = exp(-x)*(-x^2+2), y(x))
Maple raw output
[y(x) = 1/60*x^3*(x^2-20)/(x^2-2)*(-x^2+2)/exp(x)+exp(-x)*_C1+_C2*exp(-x)*x+_C3*exp(-x)*x^2]