ODE
\[ y'''(x)+3 y''(x)+3 y'(x)+y(x)=e^{-x} x \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.163228 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {1}{24} e^{-x} \left (x^4+24 c_3 x^2+24 c_2 x+24 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.038 (sec), leaf count = 36
\[\left [y \left (x \right ) = \frac {x^{4} {\mathrm e}^{-x}}{24}+{\mathrm e}^{-x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{-x} x +\textit {\_C3} \,{\mathrm e}^{-x} x^{2}\right ]\] Mathematica raw input
DSolve[y[x] + 3*y'[x] + 3*y''[x] + y'''[x] == x/E^x,y[x],x]
Mathematica raw output
{{y[x] -> (x^4 + 24*C[1] + 24*x*C[2] + 24*x^2*C[3])/(24*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) = x*exp(-x), y(x))
Maple raw output
[y(x) = 1/24*x^4/exp(x)+exp(-x)*_C1+_C2*exp(-x)*x+_C3*exp(-x)*x^2]