Chapter 14

प्रस्तावना

In this section, the introduction to the book 'Differential Equation' is provided. The book is designed according to the curriculum of Vardhman Mahaveer Open University, Kota, for the B.Sc. Second Year Mathematics Paper-II. The introduction emphasizes the importance of differential equations in mathematics and their applications in various fields such as physics, engineering, and other applied sciences. The content is structured to help students understand the fundamental concepts and methods to solve differential equations, especially focusing on first order and first degree equations in the initial units. The language of the book incorporates appropriate usage of English mathematical terminology, keeping in mind the nature of the subject. The book is also useful for students preparing for competitive examinations.

• The book is structured according to the B.Sc. Second Year Mathematics syllabus.
• It covers fundamental concepts and solution methods for differential equations.
• Emphasis is given to the use of English mathematical terms.
• The book is useful for both academic and competitive exam preparation.
• 📌 Differential Equation: An equation involving independent variable(s), dependent variable(s), and their derivatives.
• 📌 First Order: The highest derivative in the equation is of the first order.
• 📌 First Degree: The highest power of the derivative is one.

इकाई की रूपरेखा

This section outlines the structure of Unit 1: 'Differential Equation of First Order and First Degree-1'. It lists the topics that will be covered, including objectives, introduction, definitions, types of differential equations, order and degree, types of solutions, and various methods for solving first order and first degree differential equations. The outline ensures that students are aware of the topics and subtopics to be studied in this unit.

• Unit 1 covers first order and first degree differential equations.
• Topics include definitions, types, order and degree, and solution methods.
• Special focus on separation of variables and homogeneous equations.
• 📌 Order: The highest order of derivative present in the equation.
• 📌 Degree: The highest power of the highest order derivative.