ODE
\[ y''(x)+2 y'(x)+y(x)=e^{-x} \cos (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0164886 (sec), leaf count = 22
\[\left \{\left \{y(x)\to e^{-x} \left (c_2 x+c_1-\cos (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-x}} \left ( {\it \_C1}\,x+{\it \_C2}-\cos \left ( x \right ) \right ) \right \} \] Mathematica raw input
DSolve[y[x] + 2*y'[x] + y''[x] == Cos[x]/E^x,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*C[2] - Cos[x])/E^x}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = exp(-x)*cos(x), y(x),'implicit')
Maple raw output
y(x) = exp(-x)*(_C1*x+_C2-cos(x))