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Paragraph: Suppose E is the differential equation representing family of curves y^2=2 c x+2 c c where c is a positive parameter. Question: What is the order of the differential equation?

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

y^2=2 c x+2 c c Differentiate wrt x , 2 y d y d x =2 c c=y d y d x y^2=2 x y d y d x +2 (y d y d x )^ 3 / 2 y^2-2 x y d y d x =2 (y d y d x )^ 3 / 2 Squaring both sides, y^4+4 x^2 y^2 ( d y d x )^2-4 x y^3 d y d x =4 y^3 ( d y d x )^3 Clearly order =1 .

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