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) \cdot 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)

(d^{2} - 2 d + 4) y = e^{x} cos (x)

y^{^{''}} + 2 y^{^{'}} + (\frac{3}{4}) y = 3 e^{x} + (\frac{9}{2}) x

y^{^{''}} + 4 y = cos (x)

(d^{4} + d^{3} + d^{2}) y = 5 x^{2} + cos (x)

(d^{4} + d^{3} + d^{2}) y = 5 x^{2}

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)