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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

The equation of the curve for which the slope of the tangent at any point is given by x + y + 1 d y d x = 1 is (where, c is an arbitrary constant)

Options

  1. Ax y = e x - c
  2. Bx y = c e y + 2
  3. Cx = c e y - y - 2
  4. Dx = e y + y - c

Correct answer

C. x = c e y - y - 2

Step-by-step solution

The given equation is d x d y + x - 1 = y + 1 Integrating Factor = e - ∫ d y = e - y Thus, the curve is x ⋅ e − y = ∫ y + 1 e − y d y ⇒ x e - y = - y + 1 e - y - e - y + c or x = c e y - y - 2

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