What is the solution for y^{''}+y=e^t+e^{-t} ?

The solution for y^{''}+y=e^t+e^{-t} is y=c_{1}cos(t)+c_{2}sin(t)+(e^t+e^{-t})/2

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y^{''}+y=e^t+e^{-t}

y^{^{''}} + y = e^{t} + e^{- t}

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

Solution steps

y^{''} (t) + y = e^{t} + e^{- t}

Solve linear ODE:

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

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

3 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 2 = 0

y^{^{''}} + 3 y = cos (x)

y^{^{''}} + 25 y = 2 x \cdot cos (5 x)

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

y^{^{''}} - y^{^{'}} - 2 y = x, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}+y=e^t+e^{-t} ?
The solution for y^{''}+y=e^t+e^{-t} is y=c_{1}cos(t)+c_{2}sin(t)+(e^t+e^{-t})/2