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


ANSWER

$${ \phi  }^{ 2 }$$


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
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