What is the solution for y^{''}+(a+b)y=0 ?

The solution for y^{''}+(a+b)y=0 is y=c_{1}e^{sqrt(-a-b)t}+c_{2}e^{-sqrt(-a-b)t}

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y^{''}+(a+b)y=0

y^{^{''}} + (a + b) y = 0

y = c_{1} e^{- a - b t} + c_{2} e^{- - a - b t}

Solution steps

y^{''} (t) + (a + b) y = 0

Solve linear ODE:

y = c_{1} e^{- a - b t} + c_{2} e^{- - a - b t}

y = c_{1} e^{- a - b t} + c_{2} e^{- - a - b t}

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What is the solution for y^{''}+(a+b)y=0 ?
The solution for y^{''}+(a+b)y=0 is y=c_{1}e^{sqrt(-a-b)t}+c_{2}e^{-sqrt(-a-b)t}