Differential Equations Question 279
Question: The solution of the differential equation $ \frac{dy}{dx}+y\cot x=2\cos x $ is
Options:
A) $ y\sin x+\cos 2x=2c $
B) $ 2y\sin x+\cos x=c $
C) $ y\sin x+\cos x=c $
D) $ 2y\sin x+\cos 2x=c $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{dy}{dx}+y\cot x=2\cos x $
It is linear equation of the form $ \frac{dy}{dx}+Py=Q $
So, I.F. $ ={e^{\int _{{}}^{{}}{Pdx}}}={e^{\int _{{}}^{{}}{\cot xdx}}}={e^{\log \sin x}}=\sin x $
Hence the solution is $ y\sin x=\int _{{}}^{{}}{2\sin x\cos xdx+c} $
Therefore $ y\sin x=-\frac{1}{2}\cos 2x+c $
Therefore $ 2y\sin x+\cos 2x=c $ .
BETA
