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AP EAMCET202023 Sep 2020Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation tan ( y ) d x + sec 2 ( y ) · tan ( x ) d y = 0 is

Options

  1. Asin ( y ) · tan ( x ) = c
  2. Bsin ( x ) · tan ( y ) = c
  3. Csin ( x ) + tan ( y ) = c
  4. Dsin ( x ) - sin ( y ) = c

Correct answer

B. sin ( x ) · tan ( y ) = c

Step-by-step solution

tan y d x + ( sec 2 y ) ( tan x ) d y = 0 d y d x = - tan y sec 2 y tan x On integrating, we get ∫ sec 2 y d y tan y = ∫ - cot x d x ln ( tan y ) = - ln ( sin x ) + c sin x tan y = c 1

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