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Question
Choose the correct option from the given alternatives:
The solution of the differential equation `"dy"/"dx" = sec "x" - "y" tan "x"`
Options
y sec x + tan x = c
y sec x = tan x + c
sec x + y tan x = c
sec x = y tan x + c
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Solution
y sec x = tan x + c
Hint:
`"dy"/"dx" = sec "x" - "y" tan "x"`
∴ `"dy"/"dx" + "y" tan "x" = sec"x"`
I.F. = `"e"^(int "tan x dx") = "e"^(log sec "x") = sec x`
∴ the solution is
`"y" * sec"x" = int sec "x" * sec "x" "dx" + "c"`
∴ y sec x = tan x + c
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