U1L20p1 Applications of Differential Equations | LCR Circuits & SHM | 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 explore the real-world applications of Differential Equations in engineering – a very important topic for AKTU semester exams.
📌 Solutions to Previous Variation of Parameters Problems:
Problem Solution
x²y" + 2xy' - 12y = x·log x y = -x²/2·log x + x²/4 + c₁e⁻ˣ + x·log x - x + c₂x·e⁻ˣ
y" - 3y' + 2y = sin(e⁻ˣ) y = c₁eˣ + c₂e²ˣ - e²ˣ·sin(e⁻ˣ)
y" + 3y' + 2y = e^(eˣ) y = c₁/x + c₂/x² + (1/x²)·eˣ
x²y" + xy' - y = x²eˣ y = c₁x + c₂/x + (1 - 1/x)eˣ
0:00 – Solutions to Variation of Parameters problems
0:07 – Problem 1 Solution: x²y" + 2xy' - 12y = x·log x
1:06 – Problem 2 Solution: y" - 3y' + 2y = sin(e⁻ˣ)
1:32 – Problem 3 Solution: y" + 3y' + 2y = e^(eˣ)
2:07 – Problem 4 (Extra): x²y" + xy' - y = x²eˣ
2:15 – Solution: y = c₁x + c₂/x + (1 - 1/x)eˣ
3:12 – Applications of Differential Equations (Introduction)
3:34 – Application 1: Electrical Circuits
3:43 – Types of circuits: LR, CR, LC, LCR
5:33 – LR Circuit Equation: L·di/dt + R·i = E
5:59 – CR Circuit Equation: q/C + R·i = E
6:14 – LC Circuit Equation: L·di/dt + q/C = E
6:31 – LCR Circuit Equation (Most important):
7:10 – Application 2: Simple Harmonic Motion (SHM)
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 solutions to Variation of Parameters problems (exam answers)
• Real engineering applications: Circuits & SHM
• How differential equations model physical systems
• Clear derivation of circuit equations
• Perfect for AKTU semester exam preparation
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