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 = 0.0383382 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {1}{2} e^{-4 x} \left (2 e^x \left (c_2 x+c_1\right )+e^{2 x}+1\right )\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-3\,x}} \left ( {\it \_C1}\,x+\cosh \left ( x \right ) +{\it \_C2} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(-3*x)*(_C1*x+cosh(x)+_C2)