Homework for Lecture 3 of Dr. Z.’s Dynamical Models in Biology class
Email the answers (either as .pdf file or .txt file) to ShaloshBEkhad@gmail.com by 8:00pm Monday, Sept. 13, 2021. Subject: hw2 with an attachment hw2FirstLast.pdf or hw2FirstLast.txt

1.	Use Maple to solve the following differential equations for 2 ≤ k ≤ 10
	y(k)(t) − y(t) = 0	,	,y(0) = 1,y0(0) = 0,...,y(k−1)(0) = 0	.
and then find the value (in decimals) of y(1). Do you see a trend?
All y(k-1) values are = 0 after y(0). 

2.	Prove that a(n) = 2n satisfies the non-linear recurrence equation
	a(n) = a(n − 1)2	.
Is a constant multiple of 2n, C · 2n also a solution? Why?
Yes because although it is a multiple changing the value of a(n), it is still following the same series.
 
3.	Doing it both by hand and via Maple solve the recurrence, with the initial conditions
	a(n) = 3a(n − 1) − 2a(n − 2)	,	a(0) = 2	,	a(1) = 3
rsolve({a(n)-3a(n-1)+2a(n-2)=0,a(0)=2, a(1)=3},a(n))
a(n) = (2^n)+(1^n)

4.	Doing it both by hand and via Maple solve the recurrence, with the initial conditions
	a(n) = 2a(n − 1) + 2a(n − 2) − 2a(n − 3)	,	a(0) = 3	,	a(1) = 2	,	a(2) = 
rsolve({a(n)-2a(n-1)-2a(n-2)+2a(n-3)=0,a(0)=3, a(1)=2, a(2)=6},a(n))

5.	Doing it both by hand and via Maple solve the recurrence, with the initial conditions
	a(n) = a(n − 4),a(0) = 1,a(1) = 0,a(2) = 0,a(3) = 0	
rsolve({a(n)-a(n-4)=0,a(0)=1,a(1)=0,a(2)=0,a(3)=0}, a(n))