Differential Equations Question 308
Question: Solution of $ \cos x\frac{dy}{dx}+y\sin x=1 $ is
[MP PET 1999]
Options:
A) $ y\sec x\tan x=c $
B) $ y\sec x\tan x=c $
C) $ y\tan x=\sec x+c $
D) $ y\tan x=\sec x\tan x+c $
Show Answer
Answer:
Correct Answer: B
Solution:
Given equation can be written as $ \frac{dy}{dx}+y\tan x=\sec x $
$ \therefore $ I.F. $ ={e^{\int _{{}}^{{}}{\tan xdx}}}={e^{\log \sec x}}=\sec x $
Hence solution is $ y\sec x=\int _{{}}^{{}}{{{\sec }^{2}}x+c}=\tan x+c $ .
BETA
