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}

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

y^{^{'''}} + 5 y^{^{''}} + 17 y^{^{'}} + 13 y = 0

(d^{3} + d) \cdot y = 0

2 y^{^{''}} + 4 y^{^{'}} - 6 y = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y^{^{'}} (0) = 0

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