4.45.20 $y^{⁗}(x)-2y^{″}(x)+y(x)=0$

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

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00803325 (sec), leaf count = 35

$$\left\{\{y(x)\to e^{-x}(c_3{e}^{2x}+x(c_4{e}^{2x}+c_2)+c_1)\}\right\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 23

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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