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Manipal MET2021MathematicsDifferential Equations

Differential equations of the family of curves y=a x+b x , where a and b are arbitrary constants is given by

Options

  1. Ad^2 y d x^2 + y=0
  2. Bd^2 y d x^2 - ^2 y=0
  3. Cd^2 y d x^2 + ^2 y=0
  4. DNone of these

Correct answer

C. d^2 y d x^2 + ^2 y=0

Step-by-step solution

Given, y=a x+b x ...(i) On differentiating w.r.t. x , we get d y d x =-a x+b x Again, differentiating, we get d^2 y d x^2 =-a ^2 x-b^2 x=- ^2 y [from Eq. (i)] d^2 y d x^2 + ^2 y=0

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