What is the solution for x^{''}-α*x=0 ?

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

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x^{''}-α*x=0

x^{^{''}} - α \cdot x = 0

x = c_{1} e^{α t} + c_{2} e^{- α t}

Solution steps

x^{''} (t) - α \cdot x = 0

Solve linear ODE:

x = c_{1} e^{α t} + c_{2} e^{- α t}

x = c_{1} e^{α t} + c_{2} e^{- α t}

\frac{d ^{2} y}{d t ^{2}} + k^{2} y = 0

10 y^{^{''}} + 12 y^{^{'}} - 18 y = 0

y^{^{'''}} + 19 y^{^{''}} + 97 y^{^{'}} + 79 y = 0

y^{^{''}} + 3 y^{^{'}} - 16 y = 0

4 y^{^{''}} + 4 y^{^{'}} + 17 y = 0, y (0) = 2

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