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NDA 2019 Maths · Mathematics · Differential Equations · medium

The differential equation whose general solution is y=Acos 2x+Bsin 2x, where A,B are arbitrary constants, is

Single correct option

The differential equation whose general solution is y=Acos⁡2x+Bsin⁡2xy=A\cos2x+B\sin2x, where A,BA,B are arbitrary constants, is
  1. A. y′′−4y=0y''-4y=0
  2. B. y′′+4y=0y''+4y=0
  3. C. y′′+2y=0y''+2y=0
  4. D. y′+4y=0y'+4y=0
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Answer: (B) y′′+4y=0y''+4y=0

Differentiate twice: y′=−2Asin⁡2x+2Bcos⁡2xy'=-2A\sin2x+2B\cos2x and y′′=−4Acos⁡2x−4Bsin⁡2x=−4yy''=-4A\cos2x-4B\sin2x=-4y. Hence y′′+4y=0y''+4y=0. Two arbitrary constants require a second-order equation, which rules out y′+4y=0y'+4y=0. The sign must be ++ since cos⁡2x\cos 2x is oscillatory.
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Original question written in the NDA 2019 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