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JEE Main202117 Mar 2021Morning ShiftMathematicsDifferential EquationsActual

Which of the following is true for y x that satisfies the differential equation d y d x = x y - 1 + x - y ; y 0 = 0

Options

  1. Ay 1 = e - 1 2 - 1
  2. By 1 = e 1 2 - e - 1 2
  3. Cy 1 = 1
  4. Dy 1 = e 1 2 - 1

Correct answer

A. y 1 = e - 1 2 - 1

Step-by-step solution

Given d y d x = 1 + y x - 1 ⇒ d y ( y + 1 ) = x - 1 d x Integrate both the sides we get, ln y + 1 = x 2 2 - x + c Given y 0 = 0 ⇒ c = 0 ∴   y = e x 2 2 - x - 1

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