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GATE 2024 MA – Question 53

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

For y″+λy=0 on [0,π], y(0)=y′(0),y(π)=y′(π), select the listed eigenvalues.

  1. 1
  2. 2
  3. 3
  4. 4

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Correct answer: (A) 1; (D) 4

Explanation

For λ=k²>0, y=A coskx+B sinkx. First boundary gives A=kB. Substitution into the second gives $B(1+k^2)\sin(k\pi)=0$. Nonzero solutions require k a positive integer. Listed squares are **1 and 4, A,D**.

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