What is the solution for (D^4-2D^2+1)Y=cos(x) ?

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

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(D^4-2D^2+1)Y=cos(x)

(D^{4} - 2 D^{2} + 1) Y = cos (x)

Y (x) = c_{1} e^{x} + c_{2} x e^{x} + c_{3} e^{- x} + c_{4} x e^{- x} + \frac{1}{4} cos (x)

Solution steps

(D^{4} - 2 D^{2} + 1) Y (x) = cos (x)

Solve linear ODE:

Y (x) = c_{1} e^{x} + c_{2} x e^{x} + c_{3} e^{- x} + c_{4} x e^{- x} + \frac{1}{4} cos (x)

Y (x) = c_{1} e^{x} + c_{2} x e^{x} + c_{3} e^{- x} + c_{4} x e^{- x} + \frac{1}{4} cos (x)

D (D^{2} + 1) y = sin (x)

y^{^{'''}} - 2 y^{^{''}} - 5 y^{^{'}} + 6 y = 2 e^{x} (1 - 6 x)

y^{^{''}} - y^{^{'}} - 2 y = 3 e^{2 x} - 4 e^{3 x}

x^{^{''}} + 3 x^{^{'}} + 33 x = 11 cos (5 t)

y^{^{''}} + 10 y^{^{'}} + 16 y = 12 cos (2 x) + 4 sin (2 x)

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