##### 4.25.46 $$y''(x)+2 y'(x)+5 y(x)=8 \sinh (x)$$

ODE
$y''(x)+2 y'(x)+5 y(x)=8 \sinh (x)$ ODE Classiﬁcation

[[_2nd_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica
cpu = 0.225136 (sec), leaf count = 37

$\left \{\left \{y(x)\to \frac {1}{2} e^{-x} \left (e^{2 x}+2 c_2 \cos (2 x)+2 c_1 \sin (2 x)-2\right )\right \}\right \}$

Maple
cpu = 0.598 (sec), leaf count = 45

$\left [y \left (x \right ) = {\mathrm e}^{-x} \sin \left (2 x \right ) \textit {\_C2} +{\mathrm e}^{-x} \cos \left (2 x \right ) \textit {\_C1} +\frac {{\mathrm e}^{x}}{2}-{\mathrm e}^{-x}-{\mathrm e}^{-x} \cos \left (2 x \right )\right ]$ Mathematica raw input

DSolve[5*y[x] + 2*y'[x] + y''[x] == 8*Sinh[x],y[x],x]

Mathematica raw output

{{y[x] -> (-2 + E^(2*x) + 2*C[2]*Cos[2*x] + 2*C[1]*Sin[2*x])/(2*E^x)}}

Maple raw input

dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)+5*y(x) = 8*sinh(x), y(x))

Maple raw output

[y(x) = exp(-x)*sin(2*x)*_C2+exp(-x)*cos(2*x)*_C1+1/2*exp(x)-exp(-x)-exp(-x)*cos
(2*x)]