What is the solution for (d^2x)/(dt^2)=sqrt(8)x ?

The solution for (d^2x)/(dt^2)=sqrt(8)x is x=c_{1}e^{2^{3/4}t}+c_{2}e^{-2^{3/4}t}

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(d^2x)/(dt^2)=sqrt(8)x

\frac{d ^{2} x}{d t ^{2}} = 8 x

x = c_{1} e^{2^{\frac{3}{4}} t} + c_{2} e^{- 2^{\frac{3}{4}} t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} = 8 x

Solve linear ODE:

x = c_{1} e^{2^{\frac{3}{4}} t} + c_{2} e^{- 2^{\frac{3}{4}} t}

x = c_{1} e^{2^{\frac{3}{4}} t} + c_{2} e^{- 2^{\frac{3}{4}} t}

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = 8

y^{^{''}} - 5 y^{^{'}} - 6 y = 0, y (0) = 2, y^{^{'}} (0) = 5

y^{^{''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 0

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

y^{^{'''}} + 5 y^{^{'}} = 0

What is the solution for (d^2x)/(dt^2)=sqrt(8)x ?
The solution for (d^2x)/(dt^2)=sqrt(8)x is x=c_{1}e^{2^{3/4}t}+c_{2}e^{-2^{3/4}t}