Correct Answer - Option 3 : e
x - e
y = c
Formula Used:
If lnx = n, then x = en
∫ex dx = ex + c
Calculation:
\(\rm \ln\left(\frac{dy}{dx}\right)+y= x\)
⇒ \(\rm \ln\left(\frac{dy}{dx} \right)\) = x - y
⇒ \(\rm \frac{dy}{dx}\) = ex - y = \(\rm \frac{e^x}{e^y}\), which is in variable separable form.
⇒ ex dx = ey dy
Integrating both sides, we get:
⇒ ex = ey + c
∴ The solution of the differential equation is ex - ey = c.