Question

The general solution of the differential equation ${\log }_e\left(\frac{dy}{dx}\right)=x+y$ is

• (A) e^x + e^–y = C
• (B) e^x + e^y = C
• (C) e^y + e^–x = C
• (D) e^–x + e^–y = C

Answer 1

The Correct Option is A

Explanation:
$$\frac{dy}{dx}=e^x\cdot e^y\Rightarrow \int e^{-y}dy.=\int e^{x}dx\Rightarrow e^x+e^{-y}=c$$