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Systematic Elimination method to solve the system

Use the Systematic Elimination method to solve the system of ordinary differential equations.
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Consider a system of linear differential equations with constant coefficients:

where pij is a polynomial operator in , for . The three types of elementary operations are these:
(E1) Interchange two equations
(E2) Multiplying an equation through by a nonzero number
(E3) Adding to one equation a multiple of (i.e. any number times) some other equation.
We have the following theorem:

Each of the elementary operations (E1), ...

Solution Summary

The solution provides detailed explanations on the theory of Gaussian elimination method and then step-by-step calculations for the problem.

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