Question

Which of the following correctly defines ordinary differential equations?

(a) A differential equation in which a dependent variable (say ‘y’) depends on only one independent variable (say ’x’)

(b) A differential equation in which an independent variable (say ‘y’) depends on only one dependent variable (say ’x’)

(c) A differential equation in which a dependent variable (say ‘y’) depends on one or more independent variables (say ’x’, ’t’ etc.)

(d) A differential equation in which an independent variable (say ‘y’) depends on one or more dependent variables (say ’x’, ’t’ etc.)

I had been asked this question by my school teacher while I was bunking the class.

My query is from Basic Definitions in portion Ordinary Differential Equations – First Order & First Degree of Engineering Mathematics

Answer 1

Right option is (a) A differential equation in which a dependent variable (say ‘y’) depends on only one independent variable (say ’x’)

The explanation: A differential equation is an equation involving an unknown function y of one or more independent variables x, t, …… and its derivatives. These are divided into two types, ordinary or partial differential equations.

An ordinary differential equation is a differential equation in which a dependent variable (say ‘y’) is a function of only one independent variable (say ‘x’).