Differential Equations Question 260
Question: An integrating factor of the differential equation $ \sin x\frac{dy}{dx}+2y\cos x=1 $ is
Options:
A) $ {{\sin }^{2}}x $
B) $ \frac{2}{\sin x} $
C) $ \log | \sin x | $
D) $ \frac{1}{{{\sin }^{2}}x} $
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Answer:
Correct Answer: A
Solution:
[a] Given differential equation is $ \sin x\frac{dy}{dx}+2y\cos x=1;\Rightarrow \frac{dy}{dx}+2y\frac{\cos x}{\sin x}=\frac{1}{\sin x} $
$ \Rightarrow \frac{dy}{dx}+(2cotx)y=cosecx $ I.F. $ ={e^{\int{2\cot xdx}}}={e^{\int{2( \frac{\cos x}{\sin x} )dx}}}={e^{2\log \sin x}} $
$ ={e^{{\log _{e}}{{(sinx)}^{2}}}}={{(sinx)}^{2}} $
BETA
