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Repeated Eigenvalues System of Linear Differential Equation

Find the general solution for the following system:

dx/dt = 3x - y

dy/dt = 9x - 3y

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Please see the attached file.

This is a typical problem for repeated eigenvalues. To make sure you understand the theory, I have included a reference which has very nice explanation of this.
In general, a repeated value problem will have a general solution of the form:
Original equation ...

Solution Summary

The solutions provides detailed explanations on system of Linear Differential Equations and the required calculations.