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COMEDK2022MathematicsDifferential Equations

The solution of the differential equation d^2 y d x^2 =0 represents

Options

  1. Aall circles in a plane
  2. Ball straight lines in a plane
  3. Call parabolas in a plane
  4. Dall ellipses in a plane

Correct answer

B. all straight lines in a plane

Step-by-step solution

The given differential equation is d^2 y d x^2 = 0 . Integrating both sides with respect to x once, we obtain dy dx = c₁ , where c₁ is an arbitrary constant. Integrating again with respect to x , we obtain y = c₁ x + c₂ , where c₂ is another arbitrary constant. The equation y = c₁ x + c₂ represents the general equation of a straight line in the Cartesian plane, where c₁ is the slope and c₂ is the y-intercept. Answer: all straight lines in a plane

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