Formation of Differential Equations | Complete Theory, Examples & Exam Tricks скачать в хорошем качестве

Formation of Differential Equations | Complete Theory, Examples & Exam Tricks

In this lecture, we study the Formation of Differential Equations from basic to advanced level, specially designed for CSIR-NET, GATE, JAM, B.Sc, and M.Sc Mathematics students. This topic explains how to construct a differential equation by eliminating arbitrary constants or arbitrary functions from a given relation. The lecture covers full theory, step-by-step solved examples, and exam-oriented tricks to help you solve problems quickly and accurately. We begin with the fundamental concept of families of curves and understand how differentiation helps in removing arbitrary constants. Then we move towards formation using multiple constants, geometrical families (circles, straight lines, parabolas), and cases involving arbitrary functions. Special focus is given to order and degree, conceptual clarity, and common mistakes made in exams. This lecture is highly useful for mathematical modelling, physics, and engineering applications where differential equations describe real-life phenomena such as motion, heat transfer, electrical circuits, and wave propagation. ****************************************************************** Topics Covered Concept of Formation of Differential Equation Elimination of One Arbitrary Constant Elimination of Two or More Constants Formation from Family of Curves Formation involving Arbitrary Functions Order and Degree of Differential Equation Important Exam-Level Examples Shortcut Tricks for CSIR-NET & GATE Common Errors and How to Avoid Them \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ Suggested Lecture Flow (Timestamps) 00:00 Introduction & Concept 05:30 Formation with One Constant 15:00 Formation with Two Constants 28:00 Formation from Geometrical Family 40:00 Arbitrary Function Case 50:00 Order & Degree 55:00 Exam Problems & Tricks 01:05:00 Summary ========================================================= #DifferentialEquations #CSIRNETMaths #GATEMathematics #FormationOfDE #EngineeringMathematics #MathsLecture #Mathematics #JAMMaths #MScMathematics #ExamPreparation