sudden change in its input. For an increasing first-order response, one time constant in the time it takes the output to reach about 63% (~ 63.2%) of its final value, and for a decreasing response it is the time to fall to about 37% (~ 36.8%) of its initial value.

Differential equation

First-order LTI systems are characterized by the differential equation

where represents the exponential decay constant and is a function of time

The right-hand side is the forcing

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