Page 1 - CH 9 Differential Equation Lession Notes

DIFFERENTIAL EQUATIONS

9.1 Introduction
An equation involving derivatives of the dependent variable with respect to
independent variable (variables) is known as a differential equation.

9.2 Basic Concepts
In general, a differential equation is an equation involving the derivatives of some function/s such as

(i)

(ii)

are all examples of differential equations.
9.2.1. Order and degree of a differential equation
Order:
Order of a differential equation is the order of the highest order derivative occurring in the differential
equation.
Degree :
The degree of a differential equation is the power (exponent) of the highest order derivative present in the
differential equation, the derivatives present in the differential equation are made free from fractional power
and radicals.

Example: Find the order and degree of the differential equation:

Solution:

Highest order(2) derivative in above differential equation is and its index is 3.
Hence the degree of the given differential equation is 3.
9.3. General and Particular Solutions of a Differential Equation

2
Example: Verify that satisfies the differential equation (1 - x )