Mathematics

If $\phi{\left(x\right)}={\phi}^{\prime}{\left(x\right)}$ and $\phi{\left(1\right)}=2$ then $\phi{\left(3\right)}$  is equal to

${ \phi }^{ 2 }$

SOLUTION
$\phi(x) = \phi '(x) \Rightarrow \phi(x) = \frac{2\phi(x)}{dx}$

$\Rightarrow$  $\int dx = \int \frac{d(\phi (x))}{\phi(x)}$

$\Rightarrow x+c = ln \phi (x) \Rightarrow \phi (x) = k.e^{x}$

$\phi(1) = 2 \Rightarrow 2 = k.e^{1}$ $\Rightarrow k=2e^{-1}$

$\therefore \phi (x) = 2.e^{x-1}$

$\phi(3) = 2.e^{2} = \phi^{2}$

$\phi(3) = \phi^{2}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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