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Choose the correct option from the given alternatives: The solution of the differential equation dydxxyxdydx=secx-ytanx - Mathematics and Statistics

MCQ

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

Concept: Formation of Differential Equations
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 6 Differential Equations
Miscellaneous exercise 6 | Q 1.11 | Page 216
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