Hi, I am working on a home-task to analyse the properties of a ODE and its solution in a Hilbert space, and in this context I have: 1. Generated a matrix form of the ODE, and analysed its phase-portrait, eigenvalues and eigenvectors, the limits of the solution and the condition number of the matrix. 2. I have however not applied the Functional analysis of the general solution, as I am not sure how to get by this. It appears from Kreyszig "Intro to Functional Analysis" that a FUNCTIONAL can be represented in a Hilbert space. Does this mean that a FUNCTION (i.e a wavefunction) can also equally be represented in a Hilbert space? I have calculated the inner product of the ODE matrix, and defined its neither positive or negative definite value. However, which steps should I take in order to Represent the Function and general solution of the ODE in a Hilbert space? Thanks!