Correct Answer - Option 3 : e

^{x} - e

^{y} = c

**Formula Used:**

If lnx = n, then x = e^{n}

**∫**e^{x} dx = e^{x} + c

__Calculation:__

\(\rm \ln\left(\frac{dy}{dx}\right)+y= x\)

⇒ \(\rm \ln\left(\frac{dy}{dx} \right)\) = x - y

⇒ \(\rm \frac{dy}{dx}\) = e^{x - y} = \(\rm \frac{e^x}{e^y}\), which is in variable separable form.

⇒ e^{x} dx = e^{y} dy

Integrating both sides, we get:

⇒ e^{x} = e^{y} + c

**∴ The solution of the differential equation is ex - ey = c.**