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COMEDK20269 May 2026Evening ShiftMathematicsDifferential EquationsActual

The function x + y = ⁻¹ y is the solution of which of the following differential equations?

Options

  1. Ay^2 y' - y^2 + 1 = 0
  2. By^2 - 2y' + 1 = 0
  3. Cy^2 y' + y^2 + 1 = 0
  4. Dy^2 y'' - 2y' = 0

Correct answer

C. y^2 y' + y^2 + 1 = 0

Step-by-step solution

Given equation is x + y = ⁻¹ y Differentiating both sides with respect to x : 1 + y' = 1 1 + y^2 y' Multiplying both sides by 1 + y^2 : (1 + y')(1 + y^2) = y' 1 + y^2 + y' + y^2 y' = y' Subtracting y' from both sides: y^2 y' + y^2 + 1 = 0 Answer: y^2 y' + y^2 + 1 = 0

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