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Question

Mathematics for Economy Question on Differential Equations

Let a second order difference equation be
yn+2+4yn=4yn+1,n=2,3,4,......,y0=1,y1=4y_{n+2} + 4y_n = 4y_{n+1}, \, n=2,3,4,......, \,\, y_0=1, y_1=4
Then the general solution is

A

(1+n2)2n(1+n^2)2^n

B

(1+n)2n(1+n)2^n

C

(1+1n)2n(1+\frac1{n})2^n

D

(n2+n+1)2n(n^2+n+1)2^n

Answer

(1+n)2n(1+n)2^n

Explanation

Solution

The correct option is (B): (1+n)2n(1+n)2^n