Non-Homogeneous Cauchy-Euler Equations Solved | Zill ODE Exercise 4.7 Q19-24 | Step-by-Step скачать в хорошем качестве

Non-Homogeneous Cauchy-Euler Equations Solved | Zill ODE Exercise 4.7 Q19-24 | Step-by-Step

📘 Welcome to Mathematical Cafe! In this comprehensive tutorial, we solve Questions 19 through 27 from Exercise 4.7 of Dennis G. Zill's Differential Equations textbook. This video focuses exclusively on Non-Homogeneous Cauchy-Euler (Equidimensional) Equations — taking your understanding from basic homogeneous solutions to complete particular solutions. 🔍 What You'll Learn: ✅ Method of Undetermined Coefficients for Cauchy-Euler equations ✅ Variation of Parameters adapted for Cauchy-Euler form ✅ How to handle different types of non-homogeneous terms ✅ Combining complementary and particular solutions ✅ Verification techniques for non-homogeneous solutions ⚠️ Important Learning Strategy: First try solving each problem yourself! Pause after each question statement and attempt it independently before watching my solution. This builds genuine problem-solving skills. ⏱ Timestamps: 00:00 – Introduction to Non-Homogeneous Cauchy-Euler Equations 01:37 – Question : 19 - Using variation of parameters for particular solution 08:06 – Question : 20 - solved, using Undetermined Coefficients Method 11:28 – Question : 21 - repeated roots case and using variation of parameters 13:30 – How to convert to non-Homogeneous DEs to Homogenous DEs 13:54 – Question 23: Polynomial RHS (1 - constant term) 15:27 – Question 24: Polynomial RHS (-1/(x+1) term) 📚 Key Formulas Covered: Standard Cauchy-Euler form: ax²y'' + bxy' + cy = f(x) Characteristic equation: am(m-1) + bm + c = 0 General solution: y = y_c (complementary) + y_p (particular) Modified undetermined coefficients for x^m form 🔗 Resources Mentioned: Textbook: A First Course in Differential Equations by Dennis G. Zill Reference: Advanced Engineering Mathematics by Kreyszig (Section 2.10) Software: Wolfram Alpha for solution verification 📁 Study Materials & Playlists: ▶️ Complete Cauchy-Euler Series Playlist:    • Ordinary Diffrential eq Chapter 4