# This is regarding difference equations and their solutions

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1. Apr 11, 2015

### manjuvenamma

This is regarding difference equations and their solutions. And to be specific, this is about linear constant coefficient difference equations. I read at one place, that the general solution of it can be expressed as sum of homogeneous equation and the particular solution. And at another place in the same book, I read that it is expressible as the sum of zero-input solution and zero-state solution. I am confused now. What is the relationship between all the four different solution parts>

2. Apr 11, 2015

### Astronuc

Staff Emeritus
Given differential equation, from which difference equations are derived, this answers the first part, on homogenous and particular.
http://www.stewartcalculus.com/data/CALCULUS Concepts and Contexts/upfiles/3c3-NonhomgenLinEqns_Stu.pdf

Is one thinking of boundary value, initial value problems, or time-dependent vs steady-state?

Zero-input solution would simply solve for the state variables with zero input, i.e., there is no forcing function driving the system.

Zero-state would seem to imply a null initial condition.

See if this helps - http://lpsa.swarthmore.edu/Transient/TransZIZS.html

"The zero input solution is the response of the system to the initial conditions, with the input set to zero. The zero state solution is the response of the system to the input, with initial conditions set to zero."

Last edited: Apr 11, 2015