U1L18 p2 Changing of Independent Variable – More Problems | Second Order DE | BAS203 | AKTU Sem 2
ENGINEERING MATHEMATICS-II (BAS203) | AKTU B.Tech 1st Year Sem 2
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In this video lecture with notes, we continue with Method 3: Changing of Independent Variable – a very important topic where most exam questions appear.
Problems Covered in this Video:
Problem P Q R Final Equation
d²y/dx² - (1/x)dy/dx + 4x²y = x⁴ -1/x 4x² x⁴ d²y/dz² + 4y = z
d²y/dx² + cot x dy/dx + 4 cosec²x y = 0 cot x 4 cosec²x 0 Practice
x⁴ y" + 2x y' + n²y = 0 2/x n²/x⁴ 0 Practice
0:00 – More problems on Changing of Independent Variable
0:06 – Problem 1: d²y/dx² - (1/x)dy/dx + 4x²y = x⁴
1:30 – Step 1: Find Q₁ = constant
3:01 – Step 2: Find P₁
3:33 – Step 3: Find R₁
4:11 – Step 4: Write transformed equation
5:15 – Step 5: Find P.I.
5:32 – Case 5: Polynomial function → use Binomial Expansion
7:47 – Practice Problem 2: d²y/dx² + cot x dy/dx + 4 cosec²x y = 0
9:28 – Practice Problem 3: x⁴ y" + 2x y' + n²y = 0
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?
• Additional practice problems for Changing of Independent Variable
• Complete step-by-step solution of an exam-style problem
• Practice problems with answers (cosec²x and x⁴ cases)
• Clear explanation of choosing the constant for Q₁
• Perfect for AKTU semester exam preparation
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