4.43.19 $y^{‴}(x)-2y^{″}(x)+y^{\prime }(x)=e^x$

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

[[_3rd_order, _missing_y]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0232767 (sec), leaf count = 33

$$\left\{\{y(x)\to e^x((c_2-1)x+c_1-c_2+\frac{x^2}{2}+1)+c_3\}\right\}$$

Maple ✓
cpu = 0.02 (sec), leaf count = 28

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = 1/2*(x^2+(2*_C1-2)*x-2*_C1+2*_C2+2)*exp(x)+_C3