What is the solution for ((\frac{d^2f)/(dx^2))}{f(x)}=1 ?

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

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((\frac{d^2f)/(dx^2))}{f(x)}=1

\frac{( \frac{d ^{2} f}{d x ^{2}} )}{f ( x )} = 1

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

Solution steps

\frac{( \frac{d ^{2} f}{d x ^{2}} )}{f} = 1

Solve linear ODE:

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

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

y^{^{''}} = - 4 y, y (0) = 3, y^{^{'}} (0) = - 63

y^{^{''''}} - 15 y^{^{''}} + 54 y = 0

\frac{d ^{2} y}{d x ^{2}} (1) + \frac{d y}{d x} (5) + 4 y = 0

2 y^{^{''}} - 3 y^{^{'}} - 6 y = 0

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

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