How to Identify & Solve Linear Differential Equations | Diploma Engineering Maths

Master Linear Differential Equations (LDE) in this comprehensive tutorial, specifically designed for GTU Diploma Applied Mathematics and Engineering Mathematics (Semester 2) students. In this session, your mentor Priyanka Chauhan Mam from Pramey Maths Classes breaks down the identification and solution of linear equations, ensuring you are well-prepared for your university exams. This video covers the fundamental concepts of Linear Differential Equations (LDE), focusing on the identification methods and detailed solutions for both General and Particular solutions, which are crucial for scoring high marks (typically 7-8 marks in GTU exams). 📚 What You Will Learn: How to identify Linear Differential Equations in Mathematics. Understanding P and Q terms in the standard form. Step-by-step process to find the Integrating Factor (IF). Solving integration by parts (UV Rule) within LDE. Practical examples and previous year GTU exam questions for Dipoma Mathematics. 📌 Timestamps with Solved Questions: 00:00 - Intro to Linear Differential Equations & Exam Weightage 01:03 - Identifying Linear Equations & Standard Form: dy/dx + Py = Q 05:15 - Steps to Solve LDE (P, Q, and I.F.) 07:49 - Integration Formulas & Log Rules Recap 10:01 - Ex 1: dy/dx + (2/x)y = sin(x) 18:48 - Integration by Parts (U.V. Rule) Explained 24:36 - Ex 2: dy/dx + y·tan(x) = sec(x) 27:28 - Ex 3: dy/dx + y·tan(x) = cos²(x) 29:31 - Ex 4: dy/dx + y/x = x² 31:38 - Ex 5: dy/dx + y/x = eˣ, where y(0) = 2 (Particular Solution) 39:20 - Practice Questions & Conclusion 👨‍🏫 About Your Mentor: Priyanka Chauhan Mam (M.Sc, M.Phil - MATHS) is an expert in Applied Mathematics with over 16+ years of teaching experience. She is dedicated to helping Diploma Engineering students at Pramey Maths Classes master complex mathematical concepts through simple, easy-to-follow methods. Linear Differential Equation GTU Diploma Maths Sem 2 Diploma Engineering Mathematics Integrating Factor IF Priyanka Chauhan Mam Pramey Maths Classes Differential Equation Step by Step Engineering Maths Calculus GTU Exam Important Questions How to solve Linear Differential Equations Integration by Parts UV Rule Semester 2 Maths Diploma LDE Solved Examples Mathematics for Engineers Channel Name: Pramey Maths Classes Diploma Engineering Mentor: Priyanka Chauhan Mam Don't forget to LIKE, SHARE, and SUBSCRIBE for more Applied Mathematics and Diploma Engineering tutorials!