What is the solution for (D^3-3D^2+3D-1)y=0 ?

The solution for (D^3-3D^2+3D-1)y=0 is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x

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(D^3-3D^2+3D-1)y=0

(D^{3} - 3 D^{2} + 3 D - 1) y = 0

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x}

Solution steps

(D^{3} - 3 D^{2} + 3 D - 1) y = 0

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x}

8 y^{^{''}} - 9 y^{^{'}} + y = 0

y^{^{'''}} + 4 y^{^{''}} + y^{^{'}} - 26 y = 0

y^{^{''}} - 2 y^{^{'}} + 5 y = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y^{^{'}} (π) = 1, y (0) = 1

y^{^{''}} - 4 y^{^{'}} + 8 y = 0, y^{^{'}} (0) = 2

What is the solution for (D^3-3D^2+3D-1)y=0 ?
The solution for (D^3-3D^2+3D-1)y=0 is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x