Final answer:
The general form of a second-order homogeneous linear differential equation with constant coefficients is ay'' + by' + cy = 0, where 'a', 'b', and 'c' are constants and 'y' is the unknown function.
Step-by-step explanation:
The general form of a second-order homogeneous linear differential equation with constant coefficients can be written as:
ay'' + by' + cy = 0
Here, a, b, and c are constant coefficients, y is the unknown function of the variable x, and y' and y'' are the first and second derivatives of y with respect to x, respectively. This form represents a variety of physical phenomena, including mechanical oscillations and electrical circuits.
For a differential equation to be considered linear, it must satisfy two conditions: the unknown function y and its derivatives appear to the first power only and the equation does not include any products of functions or derivatives. Homogeneity refers to the absence of terms without the function y or its derivatives.