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GATE 2021 MA – Question 40

Ordinary Differential Equations · Stability and Eigenvalue Problems · 2 marks · Multiple choice

For y″+2αy′+β²y=0 with α>β>0, classify the critical point.

  1. Asymptotically stable node
  2. Asymptotically stable spiral
  3. Unstable node
  4. Unstable saddle

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Show answer and explanation

Correct answer: (A) Asymptotically stable node

Explanation

The associated system has characteristic roots −α±√(α²−β²), distinct real and both negative because √(α²−β²)<α. The origin is an **asymptotically stable node, A**.

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