What is the solution for (\frac{d^2f)/(dx^2)}{f(x)}=a^2 ?

The solution for (\frac{d^2f)/(dx^2)}{f(x)}=a^2 is f(x)=c_{1}e^{ax}+c_{2}e^{-ax}

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(\frac{d^2f)/(dx^2)}{f(x)}=a^2

\frac{\frac{d ^{2} f}{d x ^{2}}}{f ( x )} = a^{2}

f (x) = c_{1} e^{a x} + c_{2} e^{- a x}

Solution steps

\frac{\frac{d ^{2} f}{d x ^{2}}}{f} = a^{2}

Solve linear ODE:

f (x) = c_{1} e^{a x} + c_{2} e^{- a x}

f (x) = c_{1} e^{a x} + c_{2} e^{- a x}

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

4 y^{^{'''}} - 11 y^{^{''}} - 19 y^{^{'}} - 4 y = 0

y^{^{''}} - 3 y^{^{'}} = 0, y (0) = 7 - 7 e^{3}, y (1) = 0

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = 30

y^{^{''}} - 20 y^{^{'}} + 101 y = 0, y (0) = 8, y^{^{'}} (0) = 1

What is the solution for (\frac{d^2f)/(dx^2)}{f(x)}=a^2 ?
The solution for (\frac{d^2f)/(dx^2)}{f(x)}=a^2 is f(x)=c_{1}e^{ax}+c_{2}e^{-ax}