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MHT CET202619 April 2026Evening ShiftMathematicsDifferential EquationsActual

The differential equation of all lines where the length of the normal from the origin is p and the inclination of the normal is is... (where p and are arbitrary constants)

Options

  1. Ad^2y dx^2 = 0
  2. Bdy dx = 0
  3. Cdy dx = -
  4. Dd^2y dx^2 = ^2

Correct answer

A. d^2y dx^2 = 0

Step-by-step solution

The equation of a straight line in normal form is given by: x + y = p Since p and are arbitrary constants, we need to eliminate them by differentiating the equation. Differentiating once with respect to x , we get: + dy dx = 0 Differentiating again with respect to x , we get: d^2y dx^2 = 0 Since is an arbitrary constant, is not identically zero. Therefore, we must have: d^2y dx^2 = 0 Answer: d^2y dx^2 = 0

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