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Question
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.
Options
cosx
tanx
secx
sinx
Solution
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is secx.
Explanation:
The given differential equation is
`cos x * ("d"y)/("d"x) + y sinx` = 1
⇒ `("d"y)/("d"x) + sinx/cosx y = 1/cosx`
⇒ `("d"y)/("d"x) + tan x y = secx`
Here, P = tan x and Q = sec x
∴ Integrating factor = `"e"^(int Pdx)`
= `"e"^(int tan x "d"x)`
= `"e"^(log secx)`
= sec x.
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