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NDA 2016 Maths · Mathematics · Differential Equations · easy

The order of the differential equation (d^2y)/(dx^2+y=0 is 2. 2. The degree of the differential equation (dy/dx)^2+y=0 is 1.

Single correct option

Consider the following statements:
1. The order of the differential equation d2ydx2+y=0\dfrac{d^2y}{dx^2}+y=0 is 22.
2. The degree of the differential equation (dydx)2+y=0\left(\dfrac{dy}{dx}\right)^2+y=0 is 11.
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: (A) 1 only

The highest derivative in the first equation is the second, so its order is 22 and statement 1 is true. In the second equation the highest derivative dy/dxdy/dx is raised to the power 22 and the equation is polynomial in it, so the degree is 22, not 11.
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Original question written in the NDA 2016 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