U1L17 Normal Form Method | Second Order Linear DE | Normal Form vs Dependent Variable | BAS203
ENGINEERING MATHEMATICS-II (BAS203) | AKTU B.Tech 1st Year Sem 2
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In this video lecture with notes, we cover Method 2: Normal Form for solving Second Order Linear Differential Equations – used when the Changing of Dependent Variable method doesn't apply.
📌 General Form: d²y/dx² + P·dy/dx + Q·y = R
When to use Normal Form?
• When none of the conditions for Changing of Dependent Variable give zero
• i.e., 1+P+Q ≠ 0, 1-P+Q ≠ 0, P+Qx ≠ 0, etc.
0:00 – Method 2: Normal Form (Second case)
3:11 – Example 1: y" - (2/x)y' + (1 + 2/x²)y = x·eˣ
10:17 – Example 2 (Practice): x²y" - 2(x²+x)y' + (x²+x+2)y = 0
11:31 – Example 3: y" - 2 tan x y' + 5y = eˣ·sec x
This video is part of our ENGINEERING MATHEMATICS-II complete syllabus playlist for AKTU first year sem 2.
Useful for all branches – AKTU CSE, CS, IT, EC, EE, ME, CE – basically AKTU BTech first year students.
✅ Why watch?
• Complete explanation of Normal Form method
• Clear formulas for u, I, and S
• Step-by-step solved examples
• When to use which method (Normal Form vs Dependent Variable)
• Perfect for AKTU semester exam preparation
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