What is the solution for y^{''}+y-2y=2+5cos(x) ?

The solution for y^{''}+y-2y=2+5cos(x) is y=c_{1}e^x+c_{2}e^{-x}-2-5/2 cos(x)

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y^{''}+y-2y=2+5cos(x)

y^{^{''}} + y - 2 y = 2 + 5 cos (x)

y = c_{1} e^{x} + c_{2} e^{- x} - 2 - \frac{5}{2} cos (x)

Solution steps

y^{''} (x) + y - 2 y = 2 + 5 cos (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - 2 - \frac{5}{2} cos (x)

y = c_{1} e^{x} + c_{2} e^{- x} - 2 - \frac{5}{2} cos (x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{- t}

y^{^{''}} - 2 y - 4 x^{2} e^{2 x} = 0

4 y^{^{''}} + 20 y^{^{'}} + 169 y = 3, y^{^{'}} (0) = 1

y^{^{''}} - 4 y = 12 e^{2 x}

y^{^{''}} - 2 y^{^{'}} + y = 4 (x - 1) \cdot e^{- x} - 1

What is the solution for y^{''}+y-2y=2+5cos(x) ?
The solution for y^{''}+y-2y=2+5cos(x) is y=c_{1}e^x+c_{2}e^{-x}-2-5/2 cos(x)