Variable Separable Method | First Order First Degree ODE | GATE 2025 Engineering Mathematics

Welcome to the Engineering Mathematics – GATE Lecture Series! 🚀 In this video, we cover the solution of First Order, First Degree Ordinary Differential Equations (ODEs) using the Variable Separable Method – one of the simplest and most important techniques in differential equations. 📌 What you’ll learn in this video: 1. Introduction to First Order, First Degree ODEs 2. Step-by-step process of solving equations in Variable Separable Form 3. Basic definition: dy/dx = h(x)·g(y) and rearrangement into integrable form 4. Illustrations with solved examples: ✅ Example 1: dy/dx = e^(x+y) ✅ Example 2: dy/dx = x²y ✅ Example 3: dy/dx = 9x/y (Geometric interpretation – Hyperbola) 5. Handling equations of the form dy/dx = f(ax + by + c) using substitution 6. Advanced example: dy/dx = sin(x+y) solved by substitution & variable separation 7. Common mistakes to avoid in GATE & competitive exams 👉 This lecture is especially useful for GATE, ESE and other competitive exams where differential equations are frequently asked. #GATE2025 #EngineeringMathematics #DifferentialEquations #VariableSeparable #GATEMaths