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

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

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(d^4-8d)y=0

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

y = c_{1} + c_{2} e^{2 x} + e^{- x} (c_{3} cos (3 x) + c_{4} sin (3 x))

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{2 x} + e^{- x} (c_{3} cos (3 x) + c_{4} sin (3 x))

y = c_{1} + c_{2} e^{2 x} + e^{- x} (c_{3} cos (3 x) + c_{4} sin (3 x))

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

(d^{4} - d^{3} - 9 d^{2} - 11 d - 4) \cdot v = 0

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

(d^{2} - 6 d + 13) y = 0

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

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