What is the solution for (D^4-1)y=x ?

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

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(D^4-1)y=x

(D^{4} - 1) y = x

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

Solution steps

(D^{4} - 1) y = x

Solve linear ODE:

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

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

y^{^{''}} + 4 y = tan^{2} (2 x)

y^{^{''}} - 4 y = e - 2 x

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

y^{^{''}} - 3 y^{^{'}} + 2 y = x^{2} + 8 x + 9

(D^{4} - 8 D^{2} + 16) (y) = x e^{2 x}

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