Solve Difference Equation using Z-Transform | yₙ₊₂+6yₙ₊₁+9yₙ=2ⁿ | y₀=0, y₁=0 | BMATEC301 / BMATE301

Описание: 🎓 Solve Difference Equation using Z-Transform | yₙ₊₂ + 6yₙ₊₁ + 9yₙ = 2ⁿ | BMATEC301 / BMATE301 | Mathematics-III

In this video we solve the linear constant-coefficient difference equation using Z-Transform methods and given initial conditions:

Given:

yₙ₊₂ + 6yₙ₊₁ + 9yₙ = 2ⁿ , y₀=0, y₁=0

We apply the Z-transform to convert the recurrence to the z-domain, incorporate the initial conditions, solve for Y(z), and obtain y_n by taking the inverse Z-transform. The video shows full step-by-step algebra, partial fraction (or method of residues) where needed, and the final closed-form sequence — presented in VTU exam style suitable for BMATEC301 and BMATE301 students.

📚 Syllabus Reference – BMATEC301 / BMATE301 (Module 3 & 4):

Z-Transforms and standard pairs

Properties: Linearity, Shifting, Multiplication by n

Application of initial conditions in z-domain

Inverse Z-transform and sequence recovery

Solving non-homogeneous difference equations with exponential inputs

🔍 Topics Covered:
✔ Forming Y(z) using Z-transform and given initial conditions
✔ Handling the forcing term 2^n in z-domain (use of standard Z-pair)
✔ Algebraic solution for Y(z) and partial fraction for inverse transform
✔ Final expression for y_n with VTU-style explanation and exam tips

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