What is the solution for (d^2f)/(dx^2)+(df)/(dx)=0 ?

The solution for (d^2f)/(dx^2)+(df)/(dx)=0 is f(x)=c_{1}+c_{2}e^{-x}

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(d^2f)/(dx^2)+(df)/(dx)=0

\frac{d ^{2} f}{d x ^{2}} + \frac{df}{d x} = 0

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

Solution steps

\frac{d ^{2} f}{d x ^{2}} + \frac{df}{d x} = 0

Solve linear ODE:

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

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

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = - 8

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 10, y^{^{'}} (0) = 27

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 7, y^{^{'}} (0) = - 13

y^{^{'''}} - 3 y^{^{''}} + 5 y^{^{'}} + 9 y = 0

3 y^{^{''}} + 2 y^{^{'}} + y = 0

What is the solution for (d^2f)/(dx^2)+(df)/(dx)=0 ?
The solution for (d^2f)/(dx^2)+(df)/(dx)=0 is f(x)=c_{1}+c_{2}e^{-x}