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NDA 2 2024 Maths, question 89

Topic: Differential equations

Passage · Q89 to Q90

Let ydx+(x−y3)dy=0y dx+(x-y^{3}) dy=0 be a differential equation.

Q89

What are the order and degree respectively of the differential equation?

  1. (a) 1 and 1Correct answer
  2. (b) 1 and 2
  3. (c) 2 and 1
  4. (d) 1 and 3

Solution.

Answer: (a) 1 and 1

  1. Write the equation as y+(x−y³)dy/dx=0.
  2. Its highest derivative is the first derivative and appears to the first power in a polynomial equation in derivatives.
  3. Thus order=1 and degree=1; the power y³ does not determine degree.