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While I think I have a pretty good grasp on solving differential equations, I was confused about what it meant for an equation to be initially relaxed. When a system is initially relaxed, does that mean that its initial conditions are zero ($y(0) = 0$ and $y'(0) = 0$)?

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Initially relaxed means that the system is initially at rest. By that we mean that $y(0)=0$ as well as $y_n(0)=0$ where $y_n$ is the n-th derivative of the function (at the input t=0) $y$ given in that particular n-order differential equation . Hope that helped.

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