What is the solution for (x^{''})/x =a ?

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

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(x^{''})/x =a

\frac{x ^{^{''}}}{x} = a

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

Solution steps

\frac{x ^{''} ( t )}{x} = a

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = - 3

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = 3

y^{^{'''''}} + y^{^{''''}} + 9 y^{^{'''}} + 9 y^{^{''}} = 0

15 y^{^{''''}} + 92 y^{^{''}} + 64 y = 0

y^{^{''}} + 11 y^{^{'}} + 24 y = 0, y (0) = 1, y^{^{'}} (0) = - 11

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