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)

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

(d^{2} - 9) y = e^{3} x + e^{- 3} x

(d^{4} - 1) y = sin (x)

(d^{2} + 4 d - 12) y = (x - 1) e^{2} x

(d - 2)^{2} \cdot y = x^{2} - lo g_{10} (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)