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Question
General solution of `("d"y)/("d"x) + ytanx = secx` is ______.
Options
y secx = tanx + c
y tanx = secx + c
tanx = y tanx + c
x secx = tany + c
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Solution
General solution of `("d"y)/("d"x) + ytanx = secx` is y secx = tanx + c.
Explanation:
The given differential equation is `("d"y)/("d"x) + y tan x = secx`
Since, it is a linear differential equation
∴ P = tan x and Q = sec x
Integrating factor I.F. = `"e"^(int Pdx)`
= `"e"^(int tanx "d"x)`
= `"e"^(log secx)`
= sec x
∴ Solution is `y xx "I"."F". = int "Q" xx "I"."F". "d"x + "c"`
⇒ `y xx secx = int secx * secx "d"x + "c"`
⇒ `y sec x = int sec^2x "d"x + "c"`
⇒ y secx = tanx + c
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