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

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

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(d^3-2d^2-d+2)y=0

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

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

Solution steps

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

Solve linear ODE:

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

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

4 y^{^{'''}} + 17 y^{^{''}} - 16 y^{^{'}} - 5 y = 0

y^{^{''}} - y^{^{'}} - b y = 0

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

y^{^{''}} + 4 y^{^{'}} + (3^{2} + 4^{2}) y = 0

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

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