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NDA2018MathematicsDifferential EquationsActual

The differential equation of the family of curves y=p (a x)+ q ( ax ) , where p , q are arbitrary constants, is

Options

  1. Ad^2 y d x^2 +a y=0
  2. Bd^2 y d x^2 -a y=0
  3. Cd^2 y d x^2 + ay =0
  4. Dd^2 y d x^2 +a^2 y=0

Correct answer

D. d^2 y d x^2 +a^2 y=0

Step-by-step solution

aligned & y=p a x+q a x & d y d x =-p a a x+q a a x & d^2 y d x^2 =-p a^2 a x-q a^2 a x=-a^2 y & d^2 y d x^2 +a^2 y=0 aligned

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