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Question Number 1603 by 123456 last updated on 25/Aug/15

\frac{f (x)}{f^{'} (x)} = \frac{f^{'} (x)}{f (x)}

f (x) =

Answered by Rasheed Soomro last updated on 28/Aug/15

{[f^{'} (x)]}^{2} = {[f (x)]}^{2}

f^{'} (x) = \pm f (x)

L e t f (x) = y

\frac{d y}{d x} = \pm y \Rightarrow (\frac{1}{y}) \frac{d y}{d x} = \pm 1

\Rightarrow \int [(\frac{1}{y}) \frac{d y}{d x}] d x = \int (\pm 1) d x

l n ∣ y ∣ + c = \pm x + c

l n ∣ y ∣= \pm x + c

y = e^{\pm x + c} = e^{\pm x} . e^{c} = {k e}^{\pm x}

f (x) = {k e}^{\pm x}

Commented by 123456 last updated on 27/Aug/15

y = e^{\pm x + c} = e^{\pm x} e^{c} = {k e}^{\pm x}

Commented by Rasheed Soomro last updated on 27/Aug/15

Thanks for mentioning and correcting my mistake .

Pl continue same practice as I want to learn .