Differential Equations Question 356
Question: The solution of the differential equation $ \frac{dy}{dx}+\frac{1+\cos 2y}{1-\cos 2x}=0 $
[AISSE 1982; Karnataka CET 2004]
Options:
A) $ \tan y+\cot x=c $
B) $ \tan y\cot x=c $
C) $ \tan y-\cot x=c $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dy}{dx}=-\frac{1+\cos 2y}{1-\cos 2x} $
Therefore $ \frac{dy}{dx}=-\frac{2{{\cos }^{2}}y}{2{{\sin }^{2}}x} $
Therefore $ {{\sec }^{2}}ydy=-cose{c^{2}}xdx $
On integrating both sides, we get $ \tan y=\cot x+c $
Therefore $ \tan y-\cot x=c $ .
BETA
