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GATE 2026 MN – Question 13

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

Which differential equation is nonlinear, second order and first degree?

  1. $y\prime\prime+\cos x\,y\prime+e^xy=0$
  2. $y\prime\prime+\cos y=0$
  3. $y\prime\prime+\sin x=0$
  4. $(y\prime)^2+3y=0$

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Correct answer: (B) $y\prime\prime+\cos y=0$

Explanation

In B, the highest derivative is y″ and occurs to the first power, so order2 and degree1. The term cos(y) makes the equation nonlinear in the dependent variable. A and C are linear despite variable coefficients or forcing; D has only a first derivative. Thus B.

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