#Maple code for Lecture 2 of Dynamical Models in Biology (Rutgers university) , Math 336, taught by Dr. Z.

#Probelm 3 of "Getting to know you" quiz with Maple
a:=proc(n) option remember:
if n=0 then
 0:
elif n=1 then
 1:
elif n=2 then
 4:
else
 3*a(n-1)-3*a(n-2)+a(n-3):
fi:
end:

seq(a(i),i=0..10);


#Problem 4 of "Getting to know you" quiz with Maple
dsolve({D(y)(t)=1/(3*y(t)^2), y(1)=1}, y(t));

#Problem 5 of "Getting to know you" quiz with Maple
dsolve({D(D(y))(t)+y(t)=0, y(0)=0, D(y)(0)=1}, y(t));

#Problem 6 of "Getting to know you" quiz with Maple
Eigenvectors(Matrix([[7,-4],[12,-7]]));