Q8(a) Non-Homogeneous Linear DE | Operator Method | VTU 1BMATE101 2025

Описание: 📘 VTU Model Question Paper–I (2025 Scheme)
1BMATE101 – Differential Calculus & Linear Algebra
First Semester B.E./B.Tech

📍 Module-4:Ordinary differential equations of higher Order

📝 Question No. 8(a)

📘 Non-Homogeneous Linear Differential Equation | Operator Method | VTU Engineering Mathematics

In this video, we solve a second-order linear differential equation with constant coefficients using the operator method, where the RHS contains exponential and hyperbolic functions.

🧮 Problem Solved
Solve the differential equation
d²y/dx² − 4y = 3ˣ + cosh(2x − 1)

📍 Syllabus Mapping
Course: 1BMATE101 – Differential Calculus & Linear Algebra
Module 4: Ordinary Differential Equations of Higher Order
VTU 2025 Scheme

🎯 What you will learn in this video • Formation of the auxiliary equation
• Finding the complementary function (CF)
• Operator method for exponential RHS 3ˣ
• Handling hyperbolic function cosh(2x − 1) in PI
• Step-by-step particular integral calculation
• Writing the complete general solution
• Important VTU exam tips and common mistakes

📌 Why this problem is important This exact combination of exponential and hyperbolic RHS is frequently asked in VTU model question papers and university exams, making it a high-scoring problem in Module 4.

📘📘 1BMATE101 – Engineering Mathematics
🎓 VTU 2025 Scheme | Semester 1
🔥🔥 MODEL QUESTION PAPER – I (ONE-TIME COMPLETE LIST) 🔥🔥
💯 MOST IMPORTANT | MUST WATCH | EXAM FOCUSED
📄 Covers ALL 5 MODULES
🎯 Based on latest VTU pattern
⏱️ Best for revision + exam confidence
━━━━━━━━━━━━━━━━━━━━━━━
🚨🚨 FIRST – MODEL QUESTION PAPER (COMMON FOR ALL MODULES) 🚨🚨
👉 👉    • VTU Model Question Paper–I 2025 | 1BMATE10...   👈 👈
━━━━━━━━━━━━━━━━━━━━━━━
📕 MODULE 1 – Differential Calculus ✍️📈
🔥 Most Important Playlist (Must Watch)
👉    • Module 1 Differential Calculus | Polar Cur...  
⭐ Important Playlist
👉    • Differential Calculus | VTU 1BMATE101 – Mo...  
━━━━━━━━━━━━━━━━━━━━━━━
📘 MODULE 2 – Power Series, Indeterminate Forms & Multivariable Calculus 🔁📊
🔥 Partial Differentiation | Multivariable Calculus
👉    • Partial Differentiation | Multivariable Ca...  
🔥 Maclaurin’s Series Expansion | Important VTU Problems
👉    • Maclaurin’s Series Expansion | Important V...  
🔥 Maclaurin Series – Important Problems
👉    • Maclaurin Series Important Problems  
🔥 Indeterminate Forms (1^∞) – Most Important Limits
👉    • Indeterminate Forms (1^∞) – Most Important...  
⭐ Important Playlist
👉    • Power Series, Indeterminate Forms & Multiv...  
━━━━━━━━━━━━━━━━━━━━━━━
📙 MODULE 3 – Ordinary Differential Equations 🔄📐
(First Order & First Degree, Nonlinear ODEs)
🔥 ODE | VTU 1BMATE101 – Module 3
👉    • Ordinary Differential Equations (ODE) | VT...  
🔥 Solvable for P (Differential Equations)
👉    • Solvable for P (Differential Equations)  
⭐ Important Playlist (Must Watch)
👉    • Ordinary Differential Equations (ODE) of f...  
━━━━━━━━━━━━━━━━━━━━━━━
📗 MODULE 4 – Higher Order Ordinary Differential Equations 📘➕
🔥 Most Important Playlist (Must Watch)
👉    • Higher-Order Ordinary Differential Equatio...  
━━━━━━━━━━━━━━━━━━━━━━━
📕 MODULE 5 – Linear Algebra 🧮📐
🔥 Linear Algebra Made Simple – Complete
👉    • Linear Algebra Made Simple | Rank, Consist...  
📌 Note: Gauss–Jordan Method is NOT required for this syllabus
🔥 Gauss Seidel Method & Rayleigh Power Method
👉    • Gauss Seidel method and Rayleigh power method  
⭐ Important Playlist
👉    • Linear Algebra | VTU 1BMATE101 – Module 5 ...  
━━━━━━━━━━━━━━━━━━━━━━━
📝 HOW TO USE THIS (EXAM STRATEGY) 🧠🔥
1️⃣ Watch Model Question Paper – I first
2️⃣ Identify weak modules
3️⃣ Revise module playlists
4️⃣ Rewatch Model QP before exam ⏳📖
━━━━━━━━━━━━━━━━━━━━━━━
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