Differential Equations Question 342
Question: The general solution of the equation $ (e^{y}+1)\cos xdx+e^{y}\sin xdy=0 $ is
[SCRA 1986]
Options:
A) $ (e^{y}+1)\cos x=c $
B) $ (e^{y}-1)\sin x=c $
C) $ (e^{y}+1)\sin x=c $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ (e^{y}+1)\cos xdx+e^{y}\sin xdy=0 $
Therefore $ \frac{e^{y}dy}{e^{y}+1}+\frac{\cos x}{\sin x}dx=0 $
On integrating both the functions, we get $ \log (e^{y}+1)+\log (\sin x)=\log c $
Therefore $ (e^{y}+1)\sin x=c $ .
BETA
