What is the solution for (D^3-3D^2+3D-1)y=e^x+1 ?

The solution for (D^3-3D^2+3D-1)y=e^x+1 is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x+(e^xx^3)/6-1

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(D^3-3D^2+3D-1)y=e^x+1

(D^{3} - 3 D^{2} + 3 D - 1) y = e^{x} + 1

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + \frac{e ^{x} x ^{3}}{6} - 1

Solution steps

(D^{3} - 3 D^{2} + 3 D - 1) y = e^{x} + 1

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + \frac{e ^{x} x ^{3}}{6} - 1

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + \frac{e ^{x} x ^{3}}{6} - 1

y^{^{''}} - 4 y^{^{'}} = (x^{2} - 3) sin (2 x)

y^{^{''}} + 25 y = 2 sec (5 t)

2 y^{^{''}} + 3 y^{^{'}} + y = sin (x)

y^{^{''}} + 5 y^{^{'}} + 6 y = 3

y^{^{''}} - 8 y^{^{'}} + 25 y = (5 x^{3} - 7) e^{- x}

What is the solution for (D^3-3D^2+3D-1)y=e^x+1 ?
The solution for (D^3-3D^2+3D-1)y=e^x+1 is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x+(e^xx^3)/6-1