ODE
\[ y''(x)+6 y'(x)+9 y(x)=e^{-3 x} \cosh (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.209416 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {1}{2} e^{-4 x} \left (e^{2 x}+2 e^x (c_2 x+c_1)+1\right )\right \}\right \}\]
Maple ✓
cpu = 0.11 (sec), leaf count = 25
\[[y \left (x \right ) = {\mathrm e}^{-3 x} \textit {\_C2} +{\mathrm e}^{-3 x} x \textit {\_C1} +{\mathrm e}^{-3 x} \cosh \left (x \right )]\] Mathematica raw input
DSolve[9*y[x] + 6*y'[x] + y''[x] == Cosh[x]/E^(3*x),y[x],x]
Mathematica raw output
{{y[x] -> (1 + E^(2*x) + 2*E^x*(C[1] + x*C[2]))/(2*E^(4*x))}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+6*diff(y(x),x)+9*y(x) = exp(-3*x)*cosh(x), y(x))
Maple raw output
[y(x) = exp(-3*x)*_C2+exp(-3*x)*x*_C1+exp(-3*x)*cosh(x)]