Differential Equations Question 40
Question: The general solution of the differential equation $ e^{y}\frac{dy}{dx}+(e^{y}+1)\cot x=0 $ is
Options:
A) $ (e^{y}+1)\cos x=K $
B) $ (e^{y}+1)cosecx=K $
C) $ (e^{y}+1)\sin x=K $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dy}{dx}+\frac{(e^{y}+1)\cot x}{e^{y}}=0 $
Therefore $ \int _{{}}^{{}}{\frac{e^{y}}{e^{y}+1}}dy+\int _{{}}^{{}}{\cot xdx}=0 $
Therefore $ \log (e^{y}+1)+\log \sin x=\log K $
Therefore $ (e^{y}+1)\sin x=K $ .
BETA
