OBJECTIVES Students will able to Students will able to 1. define differential equation 1. define differential equation 2. identify types, order & degree of differential equation 2. identify types, order & degree of differential equation

INTRODUCTION Differential equation: Differential equation: An equation specify relation among rate of change (derivative) of variables (physical quantities)

EXAMPLES(CONT..)

EXAMPLES(CONT..)

CONTINUED

TYPES OF DIFFERENTIAL EQUATIONS Ordinary differential equation: Ordinary differential equation: If dependent variable depends on only one independent variable then it is known as Ordinary differential equation. Partial Differential equation Partial Differential equation If dependent variable depends on more than one independent variable then it is known as Partial differential equation.

EXAMPLES Ordinary differential equation Partial differential equation Ordinary differential equation Partial differential equation

ORDER AND DEGREE Order The largest derivative is known as order of differential equation Degree The degree of highest order derivative is known as degree of differential equation

EXAMPLES Equation Order Degree Equation Order Degree

SOLUTION

METHODS TO FINDING SOLUTION OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS Separable Variable Separable Variable Homogeneous differential equation Homogeneous differential equation Linear and Non Linear equation Linear and Non Linear equation Exact differential equation Exact differential equation

SEPARABLE EQUATION

INITIAL CONDITIONS In many physical problems we need to find the particular solution that satisfies a condition of the form y(x 0 )=y 0. This is called an initial condition, and the problem of finding a solution of the differential equation that satisfies the initial condition is called an initial-value problem. In many physical problems we need to find the particular solution that satisfies a condition of the form y(x 0 )=y 0. This is called an initial condition, and the problem of finding a solution of the differential equation that satisfies the initial condition is called an initial-value problem.

EXAMPLE Find a solution to y 2 = x 2 + C satisfying the initial condition y(0) = 2. Find a solution to y 2 = x 2 + C satisfying the initial condition y(0) = = C C = 4 y 2 = x 2 + 4

REFERENCE Advanced Engineering Mathematics by Erwin Kreyszig 9 th Edition, Willy International Edition Advanced Engineering Mathematics by Erwin Kreyszig 9 th Edition, Willy International Edition Differential Equation by S. L. Rose, Willy Edition Differential Equation by S. L. Rose, Willy Edition Pole online notes Pole online notes