Difference Equation with Constant Coefficients - Problem 17 | Particular Integral | Case 1 🔥

Solve y_{n+3} - 5y_{n+2} + 3y_{n+1} + 9y_n = 2^n + 3^n to find General Solution - Solved Problem #17 under Difference Equations. Welcome back to Tikle's Academy of Maths! In this 17th lecture of our series, we are solving a highly important and slightly complex third-order difference equation with constant coefficients. 📝 PROBLEM SOLVED IN THIS VIDEO: Solve: y_{n+3} - 5y_{n+2} + 3y_{n+1} + 9y_n = 2^n + 3^n This advanced numerical problem is essential for exam preparation because it covers two major challenges: 1. Finding the Complementary Function (CF) for a cubic equation using synthetic division or calculator roots. 2. Finding the Particular Integral (PI) when RHS has multiple exponential terms (2^n + 3^n), which requires handling a special "Case of Failure" for one of the parts! Whether you are preparing for B.Tech University Semester Exams (M1/M3), studying Discrete Mathematics, BSc Maths, or competitive exams like GATE, this step-by-step tutorial will clear all your practical calculation doubts. 👇 Key Concepts Covered in This Video: ✅ Converting a third-order difference equation into Shift Operator (E) form ✅ Finding roots of the cubic auxiliary equation to write the CF ✅ Splitting the PI for combined terms using PI = PI₁ + PI₂ ✅ Step-by-step resolution of the Case of Failure using shortcut shift formulas ✅ Writing the complete General Solution: y_n = CF + PI 💡 Pro-Tip for Students: Third-order equations combined with multi-term PI require maximum alertness to avoid sign mistakes. Keep your scientific calculator and dedicated practice book ready, and solve the steps along with me in the video! 📖✍️ Please SUBSCRIBE to our channel for regular educational content. Press the BELL ICON to get the latest updates instantly. Like, share with your friends, and comment down if you have any doubts! #differenceequation #particularintegral #engineeringmaths #discretemathematics #tiklesacademyofmaths #higherengineeringmathematics #gateexamprep #btechmaths #solvedproblems #problem17 #cubicrules