Chapter 1

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

This section introduces Unit 1, which focuses on differential equations of first order and first degree. The unit is structured to cover foundational concepts, types of differential equations, methods of solution, and specific forms such as equations solvable by variable separation and homogeneous equations. The outline includes objectives, definitions, types, order and degree, types of solutions, and methods for solving first order and first degree equations. The unit is designed for students to gain a thorough understanding of the basics of differential equations, especially those relevant to physics, engineering, and applied sciences. The content is aligned with the B.Sc. Part II Mathematics curriculum and is intended to prepare students for both academic and competitive examinations.

• Unit 1 covers first order and first degree differential equations.
• Topics include definitions, types, order and degree, and solution methods.
• Special focus on equations solvable by variable separation and homogeneous equations.
• Designed for foundational understanding and exam preparation.
• 📌 Differential Equation: An equation involving derivatives of a function.
• 📌 First Order: The highest derivative present is of first order.
• 📌 First Degree: The highest power of the derivative is one.

1.0 उद्देश्य (Objectives)

This section outlines the learning objectives for Unit 1. Students are expected to acquire preliminary knowledge about differential equations and learn methods to solve them. The unit specifically emphasizes first order and first degree differential equations, their special forms, and solution techniques such as variable separation and homogeneous equations. By the end of the unit, students should be able to identify, classify, and solve basic differential equations, and understand their applications in various fields.

• Learn the basics of differential equations.
• Understand methods to solve differential equations.
• Focus on first order and first degree equations.
• Study variable separation and homogeneous equations.
• 📌 Objective: The goal or purpose of the unit.