What is the solution for (D^4-81)y=0 ?

The solution for (D^4-81)y=0 is y=c_{1}e^{3x}+c_{2}e^{-3x}+c_{3}cos(3x)+c_{4}sin(3x)

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(D^4-81)y=0

(D^{4} - 81) y = 0

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

Solution steps

(D^{4} - 81) y = 0

Solve linear ODE:

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

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

y^{^{''}} + y = 0, y (0) = 3, y (1) = - 3

y^{^{''}} - 12 y^{^{'}} + a y = 0, y (0) = 1, y^{^{'}} (0) = 16

y^{^{''}} - π^{2} y = 0

y^{^{'''}} - 19 y^{^{''}} + 110 y^{^{'}} - 200 y = 0

4 y^{^{''}} + 16 y = 0

What is the solution for (D^4-81)y=0 ?
The solution for (D^4-81)y=0 is y=c_{1}e^{3x}+c_{2}e^{-3x}+c_{3}cos(3x)+c_{4}sin(3x)