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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!