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=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 = 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 = cos (x)

Solve linear ODE:

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

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