please have step by step solution Consider the following ODEs modeling causal LTI systems at initial rest, withinput x(t) and output y(t).System 1: y(t) +6dy(t) + 13y(t) =d²System 2: y(t)+6y(t) + 13y(t) =x(t) + 2x(t).x(t) — 2x(t).(a) Is System 1 stable? Is it invertible with a causal stable inverse?(b) Is System 2 stable? Is it invertible with a causal stable inverse?(c) Find an explicit time domain expression for the response of System 1 to the input x(t)5 sin(2t+1).(d) Repeat (c) for System 2. How do the two responses differ?=

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Consider the following ODEs modeling causal LTI systems at initial rest, with
input x(t) and output y(t).
System 1: y(t) +6dy(t) + 13y(t) =
d²
System 2: y(t)+6y(t) + 13y(t) =
x(t) + 2x(t).
x(t) — 2x(t).
(a) Is System 1 stable? Is it invertible with a causal stable inverse?
(b) Is System 2 stable? Is it invertible with a causal stable inverse?
(c) Find an explicit time domain expression for the response of System 1 to the input x(t)
5 sin(2t+1).
(d) Repeat (c) for System 2. How do the two responses differ?
=

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please do part d and check part c again. i dont think y(t) should be that long. is there anothere way to do it or simply it. again step by step soliutions and explain

Consider the following ODEs modeling causal LTI systems at initial rest, with
input x(t) and output y(t).
System 1: dy(t) +6ª y(t) + 13y(t) = ₫ x(t) + 2x(t).
System 2:
d2
y(t) +6ª y(t) + 13y(t) = x(t) — 2x(t).
(a) Is System 1 stable? Is it invertible with a causal stable inverse?
(b) Is System 2 stable? Is it invertible with a causal stable inverse?
(c) Find an explicit time domain expression for the response of System 1 to the input x(t)
5 sin(2t+1).
(d) Repeat (c) for System 2. How do the two responses differ?

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