Multiply by e⁻³ˣ to write (e⁻³ˣy′)′=λe⁻³ˣy. Subtract the equations for two eigenfunctions and integrate; the boundary term vanishes and (λ₁−λ₂)∫e⁻³ˣy₁y₂=0. Weight **e⁻³ˣ, A**.
More Stability and Eigenvalue Problems questions
GATE 2021 MA Q15– For y″+λy=0,0<x<π,λ>0, with y(0)=0 and y(π)−y′(π)=0, which are the eigenvalues?
GATE 2021 MA Q40– For y″+2αy′+β²y=0 with α>β>0, classify the critical point.
GATE 2025 MA Q16– For X′=MX with M any real skew-symmetric 6×6 matrix, when is the origin stable?
GATE 2024 MA Q53– For y″+λy=0 on [0,π], y(0)=y′(0),y(π)=y′(π), select the listed eigenvalues.