determine the impulse response of given second order difference equation
The impulse response of a system is its zero-state response to an impulse at the input. If the system is linear and time-invariant (LTI), then the system's response to any input signal can be described in terms of the impulse response. The impulse response only depends on the structure of the system, and it cannot depend on any initial conditions. In fact, a system with non-zero initial conditions is not linear because a part of the output (the zero-input response) does not depend on the input signal but solely on the initial conditions and the system itself.