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

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