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 = 0.0229776 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {1}{24} e^{-x} \left (24 c_3 x^2+24 c_2 x+24 c_1+x^4\right )\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac {24\,{{\rm e}^{x}} \left ( {\it \_C3}\,{x}^{2}+{\it \_C2}\,x+{\it \_C1} \right ) {{\rm e}^{-x}}+{x}^{4}}{24\,{{\rm e}^{x}}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/24*(24*exp(x)*(_C3*x^2+_C2*x+_C1)*exp(-x)+x^4)/exp(x)