Question

While an ODE of order m has m linearly independent solutions, a PDE has infinitely many.

(a) False

(b) True

This question was posed to me in a national level competition.

This intriguing question comes from Non-Homogeneous Linear PDE with Constant Coefficient topic in section Partial Differential Equations of Engineering Mathematics

Answer 1

The correct answer is (b) True

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’).

A partial differential equation is one in which a dependent variable depends on one or more independent variables.