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COMEDK2023Morning ShiftMathematicsDifferential EquationsActual

The differential equation of all non-vertical lines in a plane is

Options

  1. Ad^2 y d x^2 =0
  2. Bd^2 x d y^2 =0
  3. Cd x d y =0
  4. Dd y d x =0

Correct answer

A. d^2 y d x^2 =0

Step-by-step solution

The equation of a non-vertical line in a plane is given by y = mx + c , where m and c are arbitrary constants. Differentiating with respect to x , we get dy dx = m . Differentiating again with respect to x , we get d^2y dx^2 = 0 . Since the original equation contains two arbitrary constants, the order of the differential equation must be two. Thus, d^2y dx^2 = 0 is the required differential equation. Answer: d^2 y d x^2 =0

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