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

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

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(d^4y)/(dx^4)-16y=0

\frac{d ^{4} y}{d x ^{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

\frac{d ^{4} y}{d x ^{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^{^{''}} - 6 y^{^{'}} = 0, y (0) = 4 - 4 e^{6}, y (1) = 0

y^{^{'''}} - y^{^{''}} - 12 y^{^{'}} = 0

x^{^{''}} + 4 k^{2} x = 0

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 13, y (1) = 0

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