4.45.23 $y^{⁗}(x)+2y^{″}(x)+y(x)=24x\sin (x)$

ODE
$$y^{⁗}(x)+2y^{″}(x)+y(x)=24x\sin (x)$$ ODE Classification

[[_high_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.117397 (sec), leaf count = 46

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

Maple ✓
cpu = 0.151 (sec), leaf count = 41

$$\{y\left(x\right)=\frac{(2\mathit{\_}\mathit{C}\mathit{3}x-6x^2+2\mathit{\_}\mathit{C}\mathit{1}+3)\cos \left(x\right)}{2}-(x^3+(-\mathit{\_}\mathit{C}\mathit{4}-3)x-\mathit{\_}\mathit{C}\mathit{2})\sin \left(x\right)\}$$ 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),'implicit')

Maple raw output

y(x) = 1/2*(2*_C3*x-6*x^2+2*_C1+3)*cos(x)-(x^3+(-_C4-3)*x-_C2)*sin(x)