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Non Linear System - Second Order System

1//
Is it safe to state that for non linear system it's safe to assume/start off with x1 dot = x2?

2//
The solutions to x1 dot and x2 dot are provided in the attached. I'm unsure how to arrive at said solutions and require assistance.

Thanks in advance.

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Solution Summary

This solution is provided in 243 words in an attached .doc file. It describes a second order linear system as gives steps on how to select the state variables and their derivatives.

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