Solve Difference Equation using Z-Transform | uₙ₊₂+4uₙ₊₁+3uₙ=3ⁿ | u₀=0, u₁=1 | BMATEC301 / BMATE301

🎓 Solve Difference Equation using Z-Transform | uₙ₊₂ + 4uₙ₊₁ + 3uₙ = 3ⁿ | BMATEC301 / BMATE301 | Mathematics-III In this video, we solve a non-homogeneous linear difference equation using the Z-Transform method with given initial conditions. Given: uₙ₊₂ + 4uₙ₊₁ + 3uₙ = 3ⁿ, u₀=0, u₁=1 — Find uₙ We apply the Z-transform to convert the recurrence relation into an algebraic equation in z, substitute the initial conditions, find U(z), and then use the Inverse Z-Transform to determine the complete solution for u_n. This step-by-step derivation follows the VTU Mathematics-III syllabus for BMATEC301 / BMATE301, covering all exam-relevant concepts clearly. 📘 Syllabus Reference – BMATEC301 / BMATE301 (Module 3 & 4): Z-Transform and its properties Initial and Final Value Theorems Inverse Z-Transform using Partial Fractions Solving Linear Constant Coefficient Difference Equations Non-homogeneous case with exponential input 🔍 Topics Covered: ✔ Applying Z-transform to difference equations ✔ Using given initial conditions in z-domain ✔ Finding U(z)U(z)U(z) and performing partial fraction decomposition ✔ Taking inverse Z-transform to get unu_nun ✔ VTU-style explanation and final closed-form solution 💎 Support Us: Join our channel and get access to exclusive perks 👇 🔗    / @officialmathematicstutor   #DifferenceEquation #ZTransform #BMATEC301 #BMATE301 #MathematicsIII #VTUMathematics3 #VTUExamPreparation #VTUSyllabus #VTUMaths3 #InverseZTransform #ZTransformProblems #EngineeringMathematics #VTU2024 #VTUQuestionSolutions