4.45.27 $y^{⁗}(x)+5y^{″}(x)+6y(x)=0$

ODE
$$y^{⁗}(x)+5y^{″}(x)+6y(x)=0$$ ODE Classification

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00952887 (sec), leaf count = 50

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

Maple ✓
cpu = 0.005 (sec), leaf count = 37

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

DSolve[6*y[x] + 5*y''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[3]*Cos[Sqrt[2]*x] + C[1]*Cos[Sqrt[3]*x] + C[4]*Sin[Sqrt[2]*x] + C[2]
*Sin[Sqrt[3]*x]}}

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(y(x),x),x)+6*y(x) = 0, y(x),'implicit')

Maple raw output

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