##### 4.45.23 $$y''''(x)+2 y''(x)+y(x)=24 x \sin (x)$$

ODE
$y''''(x)+2 y''(x)+y(x)=24 x \sin (x)$ ODE Classiﬁcation

[[_high_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica
cpu = 0.24546 (sec), leaf count = 46

$\left \{\left \{y(x)\to \frac {1}{2} \left (-2 x^3+(9+2 c_4) x+2 c_3\right ) \sin (x)+\left (-3 x^2+c_2 x+3+c_1\right ) \cos (x)\right \}\right \}$

Maple
cpu = 1.455 (sec), leaf count = 45

$\left [y \left (x \right ) = \left (\frac {3}{2}-3 x^{2}\right ) \cos \left (x \right )+\left (-x^{3}+3 x \right ) \sin \left (x \right )+\textit {\_C1} \cos \left (x \right )+\textit {\_C2} \sin \left (x \right )+\textit {\_C3} x \cos \left (x \right )+\textit {\_C4} x \sin \left (x \right )\right ]$ Mathematica raw input

DSolve[y[x] + 2*y''[x] + y''''[x] == 24*x*Sin[x],y[x],x]

Mathematica raw output

{{y[x] -> (3 - 3*x^2 + C[1] + x*C[2])*Cos[x] + ((-2*x^3 + 2*C[3] + x*(9 + 2*C[4]
))*Sin[x])/2}}

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(y(x),x),x)+y(x) = 24*x*sin(x), y(x))

Maple raw output

[y(x) = (3/2-3*x^2)*cos(x)+(-x^3+3*x)*sin(x)+_C1*cos(x)+_C2*sin(x)+_C3*x*cos(x)+
_C4*x*sin(x)]