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AP EAMCET202120 Aug 2021Evening ShiftMathematicsDifferential EquationsActual

The equation of the curve passing through the point 0 , π 4 and satisfying the differential equation e x tan y d x + 1 + e x sec 2 y d y = 0 is given by

Options

  1. A1 + e x tan y = 2
  2. B1 + e x = 2 tan y
  3. C1 + e x = 2 sec y
  4. D1 + e x tan y = k

Correct answer

A. 1 + e x tan y = 2

Step-by-step solution

⇒ e x   tan y d x + 1 + e x sec 2 y d y = 0 ⇒ e x   tan y d x = - 1 + e x sec 2 y d y ⇒ e x 1 + e x d x = - sec 2 y   tan y d y Integrate both sides ∫ e x 1 + e x d x = - ∫ sec 2 y tan y d y Formula: ∫ f ' x f x d x = log   f x + c d d y tan y = sec 2 y & d d x 1 + e x = e x ⇒ log 1 + e x = - log tan y + log C ⇒ log 1 + e x + log tan y = log C ⇒ log [ 1 + e x   tan y ] = log C ⇒ 1 + e x   tan y = C The curve passing throug

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