EE102 Systems and Signals (Discussion)

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Constant Coefficients

The most common case for $a(t)$ is $a(t) = a$, a constant. In that case

$$\int_0^t a(\tau)d\tau = at$$

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Therefore, going over the steps as above, the solution to the first order differential equation with constant coefficients is:

$$y(t) = y_oe^{-at} + e^{-at}\int_0^te^{a\sigma}x(\sigma)d\sigma,   t \geq 0$$

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