Chapter 7

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

This unit introduces the foundational concepts of differential equations, specifically focusing on equations of first order and first degree. The unit is structured to systematically cover definitions, types, order and degree, and solution methods for such equations. Students will learn about the importance of differential equations in physical sciences, engineering, and applied mathematics. The unit also outlines the syllabus, including topics such as the separation of variables, homogeneous equations, and integrating factors. The learning objectives are to familiarize students with the basic terminology, classification, and solution strategies for first order, first degree differential equations.

• Introduces the concept of differential equations.
• Focuses on first order and first degree equations.
• Covers classification, order, and degree of differential equations.
• Outlines methods for solving such equations.
• 📌 Differential Equation: An equation involving independent variable, dependent variable, and their derivatives.
• 📌 First Order: The highest derivative is of first order.
• 📌 First Degree: The highest power of the derivative is one.

1.0 उद्देश्य (Objectives)

This section lists the learning objectives for the unit. It states that by the end of this unit, students will have a preliminary understanding of differential equations and methods to solve them. The focus is on first order and first degree differential equations, including their special forms, separation of variables, homogeneous equations, and equations reducible to homogeneous form. The unit aims to equip students with the skills to identify, classify, and solve such equations.

• Understand the basics of differential equations.
• Learn methods to solve first order, first degree equations.
• Study special forms and solution techniques.
• Apply separation of variables and recognize homogeneous equations.
• 📌 Separation of Variables: A method to solve differential equations by separating variables on different sides of the equation.
• 📌 Homogeneous Equation: A differential equation where all terms are of the same degree.