What is the solution for (d^4-16)y=0 ?

The solution for (d^4-16)y=0 is y=c_{1}e^{2x}+c_{2}e^{-2x}+c_{3}cos(2x)+c_{4}sin(2x)

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(d^4-16)y=0

(d^{4} - 16) y = 0

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

Solution steps

(d^{4} - 16) y = 0

Solve linear ODE:

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

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

y^{^{''}} - \frac{2}{3} y^{^{'}} + \frac{1}{9} y = 0

2 y^{^{''}} + 2 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 3

y^{^{'}} = 4 y^{^{''}}

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 5

What is the solution for (d^4-16)y=0 ?
The solution for (d^4-16)y=0 is y=c_{1}e^{2x}+c_{2}e^{-2x}+c_{3}cos(2x)+c_{4}sin(2x)