Question: 1. A causal, linear and time-invariant system, with input x(t) and output y(t), is spec- ified by the differential equation (D2 + 5D + 6)y(t)

1. A causal, linear and time-invariant system, with input x(t) and output y(t), is spec- ified by the differential equation (D2 + 5D + 6)y(t) = (D + 1)x(t) (1) (a) Find the characteristic equation, characteristic roots and characteristic (or nat- ural) modes of the system. (b) Find the impulse response of the system

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