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GATE 2023 PI – Question 12

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

Which differential equation is nonlinear?

  1. $y^{\prime\prime}+y^\prime+10y=0$
  2. $y^{\prime\prime}+(y^\prime)^2+10y=0$
  3. $y^{\prime\prime}+y^\prime+10x=0$
  4. $y^{\prime\prime}+y^\prime+10xy=0$

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Show answer and explanation

Correct answer: (B) $y^{\prime\prime}+(y^\prime)^2+10y=0$

Explanation

A linear equation contains y and its derivatives only to the first power, with coefficients depending on x. The squared derivative in **B** violates this condition. The independent forcing term in C and variable coefficient 10x in D do not make an equation nonlinear.

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