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Non Linear System - Second Order System

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

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.


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.