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NDA2019MathematicsDifferential EquationsActual

Which one of the following is the differential equation that represents the family of curves y= 1 2 x^2-c where c is an arbitrary constant?

Options

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

Correct answer

D. d y d x =-4 x y^2

Step-by-step solution

aligned & y= 1 2 x^2-c & d y d x = 0-(4 x) (2 x^2-c )^2 & =-4 x 1 (2 x^2-c )^2 & =-4 x y^2 & d y d x =-4 x y^2 aligned

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