4.45.39 $-2y^{‴}(x)+y^{⁗}(x)+2y^{″}(x)-2y^{\prime }(x)+y(x)=0$

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

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00870298 (sec), leaf count = 27

$$\left\{\{y(x)\to e^x(c_{4}x+c_3)+c_2\sin (x)+c_1\cos (x)\}\right\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 21

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = (_C2*x+_C1)*exp(x)+_C3*sin(x)+_C4*cos(x)