Question

Find the difference equation of yn = A 3^n + B 5^n.

(a) yn+2 -16 yn+1 + 15 yn-1 = 0

(b) yn+3 -14 yn+1 + 30 yn = 0

(c) 2 yn+2 -14 yn+1 + 15 yn = 0

(d) 2 yn+2 -16 yn+1 + 30 yn = 0

I had been asked this question by my college director while I was bunking the class.

I'd like to ask this question from Linear Difference Equations and Z topic in section Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

Correct answer is (d) 2 yn+2 -16 yn+1 + 30 yn = 0

For explanation I would say: This can be solved using the determinant.

\(\begin{bmatrix}

y_n & 1 & 1\\

y_{n+1} & 3 & 5\\

y_{n+2} & 9 & 25\\

\end{bmatrix} \) = 0. Now, by solving the determinant, we get the required difference equation.