What is the solution for y^{''}+2y=cos(x) ?

The solution for y^{''}+2y=cos(x) is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)+cos(x)

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y^{''}+2y=cos(x)

y^{^{''}} + 2 y = cos (x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (x)

Solution steps

y^{''} (x) + 2 y = cos (x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (x)

y^{^{''}} - 8 y^{^{'}} + 12 y = 2 x e^{2 x} - 2 x e^{- 2 x}

x^{^{''}} + x = t + 1

y^{^{''}} + 6 y^{^{'}} + 9 y = e^{3 x} ln (1 + x^{2})

y^{^{''}} + 36 y = 36 sec (6 t)

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

What is the solution for y^{''}+2y=cos(x) ?
The solution for y^{''}+2y=cos(x) is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)+cos(x)