Final answer:
The given equation is a differential equation; it involves the function y and its derivatives with respect to x.
Step-by-step explanation:
The equation x3y''' - x2y'' - 10xy' = 10y = g(x) represents a relationship between a function y and its derivatives. This type of equation is known as a differential equation because it involves derivatives of a function. Differential equations are a fundamental part of calculus and are used to describe various phenomena in the sciences and engineering. The provided equation is neither a polynomial, trigonometric, nor exponential equation based on the presence of the derivatives y''', y'', and y', which are changes to the function y with respect to the variable x.
A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable)
dy/dx = f(x)
Here “x” is an independent variable and “y” is a dependent variable
For example, dy/dx = 5x
A differential equation contains derivatives which are either partial derivatives or ordinary derivatives. The derivative represents a rate of change, and the differential equation describes a relationship between the quantity that is continuously varying with respect to the change in another quantity. There are a lot of differential equations formulas to find the solution of the derivatives.