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 = 0.0303744 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {1}{60} e^{-x} \left (60 c_3 x^2+60 c_2 x+60 c_1-x^5+20 x^3\right )\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={\frac {60\,{{\rm e}^{x}} \left ( {\it \_C3}\,{x}^{2}+{\it \_C2}\,x+{\it \_C1} \right ) {{\rm e}^{-x}}-{x}^{5}+20\,{x}^{3}}{60\,{{\rm e}^{x}}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/60*(60*exp(x)*(_C3*x^2+_C2*x+_C1)*exp(-x)-x^5+20*x^3)/exp(x)