Partial Differential Equation | Solutions of PDE by Direct Integration Method

In this powerful continuation of our Partial Differential Equations (PDE) series, we dive into the Direct Integration Method of solving PDEs — one of the foundational techniques for handling second- and third-order partial derivatives.

🔍 In this video, you’ll learn:
• What Direct Integration means in the context of PDEs
• Step-by-step solutions to real PDE problems
• How to handle boundary/initial conditions
• How to spot arbitrary functions in partial integration
• The logic behind integrating with respect to x, y, and mixed variables
• Transitioning into analytic methods: Ula’s Method, Laplace Transform & Integral Transform

🧠 Whether you’re a university student, math lover, or someone preparing for advanced exams, this video breaks down each problem slowly and clearly with detailed explanations.

📌 Make sure to watch till the end because we also preview the next topic: Analytic Methods of Solving PDEs, coming in the next episode!

🎯 Chapters (Timestamps)

00:00 - Introduction
01:15 - What We Covered in the Previous Video
02:30 - Direct Integration Method Explained
05:40 - Solved Example 1: ∂³z/∂x²∂y = cos(2x + 3y)
12:00 - Solved Example 2: ∂²z/∂x∂y = x²y
18:10 - Applying Boundary Conditions
25:00 - Example 3: ∂²z/∂y² = z
32:00 - Homogeneous Solutions with Auxiliary Equations
39:10 - Complex Example with Trig and Mixed Derivatives
48:00 - Final Example + Summary
55:00 - Introduction to Analytic Methods (Preview)
57:30 - Outro & What’s Next

🔑 Target Keywords

Use these in your title, description, tags, and when speaking in the video:
• Partial Differential Equations
• PDE by Direct Integration
• How to solve PDEs
• PDE examples with solutions
• Direct integration method
• Arbitrary functions in PDE
• PDEs step-by-step tutorial
• PDE for beginners
• Ula’s Method PDE
• Laplace Transform PDE
• Integral transform method
• PDE boundary conditions

📺 Suggested Tags

partial differential equations, solve pde, pde by direct integration, direct integration pde, how to solve pde, mathematical methods, pde solved examples, pde lecture, master talker online, differential equations, math tutorial, laplace transform pde, integral method pde, direct method pde, university math, applied math

📣 Pinned Comment (Engage Your Audience)

🔥 Which of the examples in this video helped you the most?
👇 Comment below with your question or which topic you want me to cover next — especially if it’s from PDE or Mathematical Methods!

Don’t forget to:
✅ Like
✅ Subscribe
✅ Share with your classmates!