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

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

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y^{''}-ky=0

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to - 2 lim ((x - 6)^{\frac{2}{3}})

y^{^{'}} = 0.2 ln (\frac{2000}{y}) y

\frac{d}{d x} (\frac{6}{1 + cos ( x )})

x \to \infty lim (0)

y^{^{''}} + 8 y^{^{'}} + 16 y = 5 e^{- 4 t}

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