What is the solution for x^{''}-6x=0 ?

The solution for x^{''}-6x=0 is x=c_{1}e^{sqrt(6)t}+c_{2}e^{-sqrt(6)t}

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x^{''}-6x=0

x^{^{''}} - 6 x = 0

x = c_{1} e^{6 t} + c_{2} e^{- 6 t}

Solution steps

x^{''} (t) - 6 x = 0

Solve linear ODE:

x = c_{1} e^{6 t} + c_{2} e^{- 6 t}

x = c_{1} e^{6 t} + c_{2} e^{- 6 t}

y^{^{''}} + y^{^{'}} - \frac{10}{3} y = 0

x^{^{''}} + 8 x^{^{'}} + 4 x = 0

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

4 y + 9 y^{^{''}} = - 12 y^{^{'}}

9 y^{^{''}} + 12 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for x^{''}-6x=0 ?
The solution for x^{''}-6x=0 is x=c_{1}e^{sqrt(6)t}+c_{2}e^{-sqrt(6)t}