U1L16p2 Second Order DE Solution | Integrating Factor Method | Changing of 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 complete the Changing of Dependent Variable method for solving Second Order Linear Differential Equations.
📌 Topics covered in this video:
Step Description
1 Reduce second order DE to first order linear DE
2 Identify P and Q for first order DE
3 Find Integrating Factor (I.F.) = e^(∫P dx)
4 General solution: a·(I.F.) = ∫ Q·(I.F.) dx + c
5 Find a = dv/dx, then integrate to get v
6 Final solution: y = u·v
Standard Formula for ∫ eᵃˣ·sin(bx) dx:
∫ eᵃˣ·sin(bx) dx = eᵃˣ/(a²+b²) [a·sin(bx) - b·cos(bx)]
Solved Example (continued from previous video):
• d²y/dx² - cot x dy/dx - (1 - cot x)y = eˣ·sin x
• u = eˣ, y = eˣ·v
• Reduced to: da/dx + (2 - cot x)a = sin x (where a = dv/dx)
• I.F. = e^(2x)/sin x
• Solution for a, then v, then y
Practice Problem:
• xy" - (2x-1)y' + (x-1)y = 0
• Convert to standard form and solve using same method
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 solution of a complex second order DE
• Step-by-step Integrating Factor calculation
• Standard formula for eᵃˣ·sin(bx) integration
• Practice problem for self-study
• Perfect for AKTU semester exam preparation
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