Search any question & find its solution
Question:
Answered & Verified by Expert
The general solution of a differential equation $\frac{d y}{d x}=e^{x+y}$ is :
(a) $e^x+e^{-y}=C$
(b) $e^x+e^y=C$
(c) $e^{-x}+e^y=C$
(d) $e^{-x}+e^{-y}=C$
(a) $e^x+e^{-y}=C$
(b) $e^x+e^y=C$
(c) $e^{-x}+e^y=C$
(d) $e^{-x}+e^{-y}=C$
Solution:
1517 Upvotes
Verified Answer
(a) $\frac{d y}{d x}=e^x \cdot e^y \Rightarrow \int e^{-y} d y=\int e^x d x$
$$
\Rightarrow-e^{-y}=e^x+k \Rightarrow e^x+e^{-y}=C
$$
$$
\Rightarrow-e^{-y}=e^x+k \Rightarrow e^x+e^{-y}=C
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.