Linear Differential Equations of First Order

Linear Differential Equations of First Order Dr. J. Girish Kumar Lecturer in Mathematics Government Degree College Jammalamadugu

Commissionerate of Collegiate Education Applications of Linear Differential Equations: The Hanging Chain, Pursuit Curves Simple Electric Circuits Newton’s Law of Cooling Dr. J. Girish Kumar

Commissionerate of Collegiate Education Definition: Dr. J. Girish Kumar

Commissionerate of Collegiate Education Dr. J. Girish Kumar

Commissionerate of Collegiate Education Theorem: Dr. J. Girish Kumar

Commissionerate of Collegiate Education Proof: Given linear differential equation is …(1) Where ‘P’ and ‘Q’ are functions of ‘x’ alone Dr. J. Girish Kumar

Commissionerate of Collegiate Education …(2) and Dr. J. Girish Kumar

Commissionerate of Collegiate Education (function of ‘x’ alone) Dr. J. Girish Kumar

Commissionerate of Collegiate Education Integrating on both sides, we get Dr. J. Girish Kumar

Commissionerate of Collegiate Education and Where Dr. J. Girish Kumar

Commissionerate of Collegiate Education The general solution of the given differential equation is Dr. J. Girish Kumar

Commissionerate of Collegiate Education Definition: Dr. J. Girish Kumar

Commissionerate of Collegiate Education Where and Dr. J. Girish Kumar

Commissionerate of Collegiate Education The general solution of the given differential equation is Dr. J. Girish Kumar

Linear Differential Equations of First Order

Linear Differential Equations of First Order

Presentation Transcript

First Order Linear Differential Equations

Chapter 1: First-Order Differential Equations

First-Order Differential Equations

Chapter 1: First-Order Differential Equations

Chapter 1: First-Order Differential Equations

SECOND-ORDER DIFFERENTIAL EQUATIONS

SECOND-ORDER DIFFERENTIAL EQUATIONS

First Order Linear Differential Equations

Chapter 1 First-Order Differential Equations

Systems of Linear Differential Equations

LINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

First-Order Differential Equations

Chapter 2 Differential Equations of First Order

Chapter 2 Theory of First Order Differential Equations

Solving First-Order Differential Equations

First-order linear equations

First-Order Differential Equations

Chap 1 First-Order Differential Equations

First Order Partial Differential Equations

First-order linear equations

Linear higher-order Differential Equations

First Order Linear Equations