GATE Ordinary Differential Equations: Stability and Eigenvalue Problems – Previous Year Questions

5 GATE previous year questions on Stability and Eigenvalue Problems (Ordinary Differential Equations, Mathematics) with answers and explanations, from every paper.

1. GATE 2021 MA Q15 (1 mark, Multiple choice) – For y″+λy=0,0<x<π,λ>0, with y(0)=0 and y(π)−y′(π)=0, which are the eigenvalues?
2. GATE 2021 MA Q40 (2 marks, Multiple choice) – For y″+2αy′+β²y=0 with α>β>0, classify the critical point.
3. GATE 2022 MA Q20 (1 mark, Multiple choice) – Eigenfunctions at distinct eigenvalues of y″−3y′=λy,0<x<π, with y(0)=y(π)=0 are orthogonal with which weight?
4. GATE 2024 MA Q53 (2 marks, Multiple select) – For y″+λy=0 on [0,π], y(0)=y′(0),y(π)=y′(π), select the listed eigenvalues.
5. GATE 2025 MA Q16 (1 mark, Multiple choice) – For X′=MX with M any real skew-symmetric 6×6 matrix, when is the origin stable?