What is the solution for 2y-y^{''}=0 ?

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

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2y-y^{''}=0

2 y - y^{^{''}} = 0

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

Solution steps

2 y - y^{''} (t) = 0

Solve linear ODE:

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

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

2 y = 3 y^{^{''}}

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 1

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

x^{^{'''}} + 5 x^{^{''}} - 25 x^{^{'}} - 125 x = 0

y^{^{''}} - 12 y^{^{'}} + 35 y = 0, y (0) = e^{k x}

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