4.45.38 $2y^{‴}(x)+y^{⁗}(x)-2y^{\prime }(x)-y(x)=0$

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

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00860763 (sec), leaf count = 32

$$\left\{\{y(x)\to e^{-x}(c_3{x}^2+c_{2}x+c_4{e}^{2x}+c_1)\}\right\}$$

Maple ✓
cpu = 0.009 (sec), leaf count = 24

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

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

Mathematica raw output

{{y[x] -> (C[1] + x*C[2] + x^2*C[3] + E^(2*x)*C[4])/E^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(y(x),x)-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C4*x^2+_C3*x+_C2)*exp(-x)+_C1*exp(x)