Resolution of linear constant coefficient difference equation (homogeneus + particular)

1. Which is a homogeneous linear differential equation with constant coefficients?
2. What is linear constant coefficient difference equations?
3. What is linear differential equation with example?

Which is a homogeneous linear differential equation with constant coefficients?

P(t)y″+Q(t)y′+R(t)y=G(t). y″+p(t)y′+q(t)y=g(t). We call a second order linear differential equation homogeneous if g(t)=0.

What is linear constant coefficient difference equations?

The general linear difference equation of order r with constant coefficients is –(E)un = f (n) (1) where –(E) is a polynomial of degree r in E and where we may assume that the coefficient of Er is 1.

What is linear differential equation with example?

dy/dx + Py = Q where y is a function and dy/dx is a derivative. The solution of the linear differential equation produces the value of variable y. Examples: dy/dx + 2y = sin x.