What is the solution for y^{''}-αy=0 ?

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

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y^{''}-αy=0

y^{^{''}} - α y = 0

y = c_{1} e^{α t} + c_{2} e^{- α t}

Solution steps

y^{''} (t) - α y = 0

Solve linear ODE:

y = c_{1} e^{α t} + c_{2} e^{- α t}

y = c_{1} e^{α t} + c_{2} e^{- α t}

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = x e^{- x} ln (x)

25 y^{^{''}} + 80 y^{^{'}} + 64 y = 0, y^{^{'}} (0) = 5

y^{^{'''}} + 9 y^{^{''}} + 22 y^{^{'}} + 14 y = 0

y^{^{''}} + y^{^{'}} + 2 y = 0, y (0) = y^{^{'}} (0)

y^{^{''}} + 36 y^{^{'}} = 0, y (0) = 1, y (0) = 0

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