Is non-causal, non-LTI solution to difference equation correct?

1. How do you know if a differential equation is linear time invariant?
2. How do you determine the causality of a system?
3. What is differential equation in signals and systems?

How do you know if a differential equation is linear 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.

How do you determine the causality of a system?

A system is said to be causal if it does not respond before the input is applied. In other words, in a causal system, the output at any time depends only on the values of the input signal up to and including that time and does not depend on the future values of the input.

What is differential equation in signals and systems?

Differential systems form the class of systems for which the input and output signals are related implicitly through a linear, constant coefficient ordinary differential equation. − ( ) + ( ) , where the derivative of the velocity is the car's acceleration. Rearranging this equation, we obtain (1).