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

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