Confusion regarding application of time invariance to flip system?

1. What is the condition for time-invariant system?
2. What is meant by time invariance?
3. What is time-invariant in digital signal processing?
4. How do you know if a differential equation is time-invariant?

What is the condition for time-invariant system?

A system is time-invariant if its output signal does not depend on the absolute time. In other words, if for some input signal x(t) the output signal is y1(t)=Trx(t), then a time-shift of the input signal creates a time-shift on the output signal, i.e. y2(t)=Trx(t−t0)=y1(t−t0).

What is meant by time invariance?

Mathematically speaking, "time-invariance" of a system is the following property: Given a system with a time-dependent output function , and a time-dependent input function , the system will be considered time-invariant if a time-delay on the input directly equates to a time-delay of the output function.

What is time-invariant in digital signal processing?

A time-invariant system is one where a time delay (or shift) in the input sequence causes an equivalent time delay in the system's output sequence.

How do you know if a differential equation is time-invariant?

A linear differential equation with constant coefficients displays time invariance. If we use the same input and starting conditions for a system now or at some later time then the result relative to the initial starting time will be identical.