What is the solution for y^{''''}-y=cos(x) ?

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

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y^{''''}-y=cos(x)

y^{^{''''}} - y = cos (x)

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

Solution steps

y^{(4)} (x) - y = cos (x)

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} - 2 y = 2 x + 2

y^{^{''}} + 10 y^{^{'}} + 9 y = 6 cos (3 t + 1.5708) H (t)

\frac{d ^{2} y}{d x ^{2}} + 4 y = tan (2 x)

y^{^{''''}} + 2 y^{^{''}} + 1 = 0

y^{^{''}} - 2 y^{^{'}} + y = x^{2} + 1

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