Introduction to Differential Equations

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Presentation transcript:

Introduction to Differential Equations

ordinary differential equations Definition: A differential equation is an equation containing an unknown function and its derivatives. Examples:. 1. 2. 3. y is dependent variable and x is independent variable, and these are ordinary differential equations

Partial Differential Equation Examples: 1. u is dependent variable and x and y are independent variables, and is partial differential equation. 2. 3. u is dependent variable and x and t are independent variables

Order of Differential Equation The order of the differential equation is order of the highest derivative in the differential equation. Differential Equation ORDER 1 2 3

Degree of Differential Equation The degree of a differential equation is power of the highest order derivative term in the differential equation. Differential Equation Degree 1 1 3

Linear Differential Equation A differential equation is linear, if 1. dependent variable and its derivatives are of degree one, 2. coefficients of a term does not depend upon dependent variable. Example: 1. is linear. Example: 2. is non - linear because in 2nd term is not of degree one.

3. 4. is non – linear Example: Example: is non - linear because in 2nd term coefficient depends on y. 3. Example: 4. is non – linear is non - linear because

It is Ordinary/partial Differential equation of order… and of degree…, it is linear / non linear, with independent variable…, and dependent variable….

1st – order differential equation 1. Derivative form: 2. Differential form: . 3. General form: or Classfication of Differential Equation

First Order Ordinary Differential equation

Second order Ordinary Differential Equation Classfication of Differential Equation

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