A) \[y\sec x\tan x=c\]
B) \[y\sec x\tan x=c\]
C) \[y\tan x=\sec x+c\]
D) \[y\tan x=\sec x\tan x+c\]
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 \[y\sec x=\int_{{}}^{{}}{{{\sec }^{2}}x+c}=\tan x+c\].
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