Differential Equations Question 327
Question: The solution of the differential equation $ (\sin x+\cos x)dy+(\cos x-\sin x)dx=0 $ is
Options:
A) $ e^{x}(\sin x+\cos x)+c=0 $
B) $ e^{y}(\sin x+\cos x)=c $
C) $ e^{y}(\cos x-\sin x)=c $
D) $ e^{x}(\sin x-\cos x)=c $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{dy}{dx}=-\frac{\cos x-\sin x}{\sin x+\cos x} $
Therefore $ dy=-( \frac{\cos x-\sin x}{\sin x+\cos x} )dx $
On integrating both sides, we get
Therefore $ y=-\log (\sin x+\cos x)+\log c $
Therefore $ y=\log ( \frac{c}{\sin x+\cos x} ) $
Therefore $ e^{y}(\sin x+\cos x)=c $ .
BETA
