Chapter 15

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

This section introduces the study of differential equations, focusing specifically on those of first order and first degree. It outlines the structure of the unit, which includes objectives, definitions, types of differential equations, order and degree, types of solutions, and methods for solving such equations. The section also provides a roadmap for the topics to be covered, including separation of variables, homogeneous equations, and equations reducible to homogeneous form. The unit is designed to give students foundational knowledge of differential equations and equip them with methods to solve first order, first degree equations, which are commonly encountered in physics, engineering, and applied sciences.

• Introduction to differential equations of first order and first degree.
• Overview of key topics: definitions, types, order and degree, solution methods.
• Emphasis on practical solution techniques such as separation of variables.
• 📌 Differential Equation: An equation involving independent variable(s), dependent variable(s), and their derivatives.
• 📌 First Order: The highest derivative present is of first order.
• 📌 First Degree: The highest power of the derivative is one.

1.0 उद्देश्य (Objectives)

In this section, the objectives of the unit are clearly stated. Students will gain preliminary knowledge about differential equations and learn methods to solve them. The focus is on equations of first order and first degree, including their special forms and solution methods such as separation of variables, homogeneous equations, and equations reducible to homogeneous form. By the end of this unit, students will be able to identify, classify, and solve basic differential equations relevant to various scientific and engineering problems.

• Understand the basic concepts of differential equations.
• Learn methods to solve first order, first degree differential equations.
• Study special forms such as homogeneous equations.
• Apply separation of variables and other solution techniques.
• 📌 Separation of Variables: A method to solve differential equations by separating the variables on different sides of the equation.