Lagrange's Linear PDE | Multiplier Method Made Easy-Problem 3|SNS Institutions

🎓 Welcome to our chennel In this video, we’re going to learn how to solve Lagrange's Linear Partial Differential Equation using the Multiplier Method — in a clear, simple, and easy-to-understand way. 📘 What You’ll Learn in This Video: ✅ What is Lagrange's Linear PDE ✅ What is the standard form: Pp + Qq = R ✅ When to use the Multiplier Method ✅ Step-by-step solving technique ✅ A solved example with detailed explanation ✅ Tips to avoid common mistakes ✅ How to check your solution ✍️ What is Lagrange's Linear PDE? A first-order PDE of the form: 👉 P(x, y, z)·p + Q(x, y, z)·q = R(x, y, z) Where: p = ∂z/∂x q = ∂z/∂y P, Q, R are functions of x, y, z This equation can be solved using the Method of Characteristics or the Multiplier Method (when it's hard to solve directly). 🧠 What is the Multiplier Method? Sometimes, the equations dx/P = dy/Q = dz/R are hard to solve directly. In such cases, we choose suitable multipliers (l, m, n) such that: 👉 l·P + m·Q + n·R = 0 This simplifies the system and helps us solve it more easily! #LagrangeMethod #MultiplierMethod #PDE #PartialDifferentialEquations #EngineeringMath