What is the solution for (d^3-d^2-4d+4)y=0 ?

The solution for (d^3-d^2-4d+4)y=0 is y=c_{1}e^x+c_{2}e^{-2x}+c_{3}e^{2x}

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(d^3-d^2-4d+4)y=0

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

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

Solution steps

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

Solve linear ODE:

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

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

4 y^{^{''}} + \frac{1}{784} y = 0, y (0) = 7

64 y^{^{''}} + 144 y^{^{'}} + 83 y = 0

x^{^{''}} + 2 \cdot x^{^{'}} + x = 0

0.2 x^{^{''}} + 4 x^{^{'}} + 20 x = 0

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

What is the solution for (d^3-d^2-4d+4)y=0 ?
The solution for (d^3-d^2-4d+4)y=0 is y=c_{1}e^x+c_{2}e^{-2x}+c_{3}e^{2x}