4.45.40 $2y^{‴}(x)+y^{⁗}(x)+3y^{″}(x)+2y^{\prime }(x)+y(x)=0$

ODE
$$2y^{‴}(x)+y^{⁗}(x)+3y^{″}(x)+2y^{\prime }(x)+y(x)=0$$ ODE Classification

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0103851 (sec), leaf count = 52

$$\left\{\{y(x)\to e^{-x/2}((c_{2}x+c_1)\sin \left(\frac{\sqrt{3}x}{2}\right)+(c_{4}x+c_3)\cos \left(\frac{\sqrt{3}x}{2}\right))\}\right\}$$

Maple ✓
cpu = 0.005 (sec), leaf count = 36

$$\{y\left(x\right)=((\mathit{\_}\mathit{C}\mathit{4}x+\mathit{\_}\mathit{C}\mathit{2})\cos \left(\frac{\sqrt{3}x}{2}\right)+\sin \left(\frac{\sqrt{3}x}{2}\right)(\mathit{\_}\mathit{C}\mathit{3}x+\mathit{\_}\mathit{C}\mathit{1})){\mathrm{e}}^{-\frac{x}{2}}\}$$ Mathematica raw input

DSolve[y[x] + 2*y'[x] + 3*y''[x] + 2*y'''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 0, y(x),'implicit')

Maple raw output

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