What is the solution for (4d^4-8d^3-4d^2+8d)y=0 ?

The solution for (4d^4-8d^3-4d^2+8d)y=0 is y=c_{1}+c_{2}e^{2x}+c_{3}e^{-x}+c_{4}e^x

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(4d^4-8d^3-4d^2+8d)y=0

(4 d^{4} - 8 d^{3} - 4 d^{2} + 8 d) y = 0

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{- x} + c_{4} e^{x}

Solution steps

(4 d^{4} - 8 d^{3} - 4 d^{2} + 8 d) y = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{- x} + c_{4} e^{x}

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{- x} + c_{4} e^{x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 4, y^{^{'}} (0) = - 15

4 y^{^{''}} + π^{2} y = 0

3 y^{^{'''}} + 2 y^{^{''}} = 0

2 y^{^{''}} + 28 y^{^{'}} + 99 y = 0, y (0) = 2, y^{^{'}} (0) = 0

What is the solution for (4d^4-8d^3-4d^2+8d)y=0 ?
The solution for (4d^4-8d^3-4d^2+8d)y=0 is y=c_{1}+c_{2}e^{2x}+c_{3}e^{-x}+c_{4}e^x