Chapter 6

प्रस्तावना

The preface introduces the textbook 'Differential Equations' as designed according to the curriculum of Vardhman Mahaveer Open University, Kota, for the B.Sc. Second Year Mathematics Paper II. The preface emphasizes the practical nature of mathematics and the careful use of English terminology throughout the book. It acknowledges the contributions of various scholars who have authored the different units and expresses gratitude to the authors of standard references used in the preparation of the text. The book is also intended to serve as a useful guide for students preparing for competitive examinations.

• Textbook is tailored for B.Sc. Second Year Mathematics, Paper II.
• English terminology is used appropriately for clarity.
• Content is based on standard references and authored by subject experts.
• Useful for both university studies and competitive exams.
• 📌 Preface: An introductory note explaining the purpose, scope, and acknowledgments related to the textbook.

इकाई 1: प्रथम घात एवं प्रथम कोटि के अवकल समीकरण-1 (Differential Equation of First Order And First Degree-1)

This unit focuses on first order and first degree differential equations. It outlines the structure of the unit, which includes objectives, introduction, definitions, types of differential equations, order and degree, types of solutions, and methods for solving such equations. The unit also covers special forms, variable separation, homogeneous equations, and equations reducible to homogeneous form. The structure ensures a step-by-step approach to understanding and solving first order, first degree differential equations.

• Covers first order and first degree differential equations.
• Includes definitions, types, order, degree, and solution methods.
• Discusses variable separation and homogeneous equations.
• Provides a systematic approach for learning.
• 📌 First Order Differential Equation: An equation involving the first derivative of the dependent variable with respect to the independent variable.
• 📌 First Degree Differential Equation: An equation where the highest power of the derivative is one.