What is the differential equation of all parabolas having their vertex at the origin and axis along the positive -axis, ()?

Answer and explanation

Correct answer: B.

  1. Step 1: Start with the equation of the family: .
  2. Step 2: Differentiate with respect to : .
  3. Step 3: Substitute back into : . Divide by (): .
Answer
.
Why not the others: has an incorrect positive sign; inverts the factor of ; is the equation for straight lines.

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