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NDA 2024 Maths · Mathematics · Differential Equations · medium

The differential equation y''+sin y'=0 has degree 1. 2. The differential equation of the family y=ax^2+bx (a,b arbitrary constants) is of order 2.

Single correct option

Consider the following statements:
1. The differential equation y′′+sin⁡y′=0y''+\sin y'=0 has degree 1.
2. The differential equation of the family y=ax2+bxy=ax^2+bx (a,ba,b arbitrary constants) is of order 2.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (B) 2 only

Degree is defined only when the equation is a polynomial in the derivatives. Because sin⁡y′\sin y' is not a polynomial in y′y', the degree is not defined, so statement 1 is false. A family with two arbitrary constants has a differential equation of order 2, so statement 2 is true. Trap: reading the power of y′′y'' as 1 and calling the degree 1.
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Original question written in the NDA 2024 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake