4.45.18 $y^{⁗}(x)+y^{″}(x)+y(x)=0$

ODE
$$y^{⁗}(x)+y^{″}(x)+y(x)=0$$ ODE Classification

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00933399 (sec), leaf count = 56

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

Maple ✓
cpu = 0.005 (sec), leaf count = 47

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

DSolve[y[x] + y''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = (_C2*exp(1/2*x)+_C4*exp(-1/2*x))*cos(1/2*3^(1/2)*x)+sin(1/2*3^(1/2)*x)*(_
C1*exp(1/2*x)+_C3*exp(-1/2*x))