Lect-26: Homogeneous Linear Partial Differential Equation – Pattern 3

📘 Lect-26: Homogeneous Linear Partial Differential Equation – Pattern 3 In this Mathematics lecture (Lecture 26), we solve a very important and exam-oriented question based on Homogeneous Linear Partial Differential Equations using the operator method 📐. The lecture focuses on the standard Pattern-3 type equation: (D³ − 4D²D′ + 4D′D²)z = 4 sin(2x + y) This type of operator-based PDE is frequently asked in university examinations and competitive exams like GATE 📝. The complete solution is explained step by step so that students can clearly understand the concept and apply the method confidently in exams. This lecture is taught by Renuka Ma’am 👩‍🏫, who is known for her simple teaching style and ability to break down complex Engineering Mathematics topics into easy-to-understand steps ✨. 🎓 This lecture is useful for students of: • BCA • MCA • BSc Mathematics • BTech / BE (Engineering Mathematics) • GATE aspirants 🚀 • Other university and competitive exam students 📌 What you will learn in this lecture: • Homogeneous Linear Partial Differential Equation using operator method • Pattern-3 type PDE problems • Step-by-step solution of (D³ − 4D²D′ + 4D′D²)z = 4 sin(2x + y) • Handling trigonometric RHS in PDE • Exam-oriented approach to score better marks 💯 🏫 This lecture is especially helpful for students studying under universities such as: • CSVTU (Chhattisgarh Swami Vivekanand Technical University) • AKTU (Dr. A.P.J. Abdul Kalam Technical University) • KTU (APJ Abdul Kalam Technological University) • PTU (Punjab Technical University) • UTU (Uttarakhand Technical University) • and other Indian universities following the Engineering Mathematics syllabus 📚 🎯 If you are revising Partial Differential Equations or preparing for semester exams or GATE, this lecture will help you gain strong conceptual clarity and confidence 💪. ▶️ Watch the complete lecture for full understanding 👍 Like | 🔔 Subscribe | 💬 Comment for doubts or more important questions