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This question was previously asked in

NDA (Held On: 6 Sep 2020) Maths Previous Year paper

- y = e
^{x}+ c - y = e
^{-x}+ c - y = ln x + c
- y = 2 ln x + c

Option 1 : y = e^{x} + c

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__Concept:__

__\(\rm \int e^{x} \;dx = e^{x} + c\)__

__Calculation:__

Given:

\(\ln \rm \left(\dfrac{dy}{dx}\right)=x\)

⇒ \(\rm \frac{dy}{dx} = e^{x}\)

⇒ dy = e^{x} dx

Integrating both sides, we get

\(\Rightarrow \rm \int dy = \int e^{x} \;dx\)

⇒ y = e^{x} + c

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