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Differential Equation : Solve Using Classical Method; Identify Critically Damp, Overdamped or Under-Damped

X'' + 2x' + x = 5exp(-t) + t for t greater/equal to zero; x(0)=2; x'(0)=1

and identify critically damp, over-damped or under-damped (overdamped or underdamped).
thank you

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Solution Summary

The solution of a differential equation is found and damping is investigated. The solution is detailed and well presented.