Kenyon College
paquind@kenyon.edu
Math 333
Quiz 1
Tuesday, January 22, 2008
1. Consider the population model
dP
= 0.4P
dt
1
P
100
P
1 ,
25
where P (t) is the population at time t.
(a) For what values of P is the population in equilibrium?
(b) For what val
Kenyon College
paquind@kenyon.edu
Math 333
Quiz 6
Thursday, March 20, 2008
1. Find the general solution of the dierential equation 6y y y = 0.
2. Find the general solution of the dierential equation y + 2y 8y = 0.
3. Find the general solution of the diere
Kenyon College
paquind@kenyon.edu
Math 333
Quiz 7
Thursday, March 27, 2008
1. Find the general solution of the dierential equation
y + 7y + 10y = e2t .
2. Find the general solution of the dierential equation
y 5y + 4y = e4t .
Math 333: Di Eq
1
Quiz 7
Keny
Kenyon College
paquind@kenyon.edu
Math 333
Quiz 5
Thursday, February 21, 2008
1. Find the general solution of the dierential equation
y + 2y 3y = 0.
2. Determine the values of , if any, for which all solutions of the dierential
equation
y (2 1)y + ( 1)y =
Kenyon College
paquind@kenyon.edu
Math 333
Quiz 4
Thursday, February 14, 2008
1. Find all equilibrium points of the system
dx
= x y + x2 xy
dt
dy
= = y + x2 .
dt
2. Convert the second-order dierential equation
dy
d2 y
+ 7 + 10y = 0
dt2
dt
into a system of
Kenyon College
paquind@kenyon.edu
Math 333
Quiz 2
Thursday, January 31, 2008
1. Sketch the phase line for the dierential equation
dy
= (y 1)(y 2)(y 3).
dt
Identify each equilibrium point as a sink, source, or node.
2. Find a polynomial function f (y ) of
Kenyon College
paquind@kenyon.edu
Math 333
Quiz 3
Thursday, February 7, 2008
1. Locate the bifurcation values for
dy
= y 2 ay + 1
dt
and describe the bifurcation that occurs at each bifurcation value.
Math 333: Di Eq
1
Quiz 3
Kenyon College
paquind@kenyon
Kenyon College
paquind@kenyon.edu
Math 333
Quiz 7 Solutions
Thursday, March 27, 2008
1. Find the general solution of the dierential equation
y + 7y + 10y = e2t .
1 2t
e
28
2. Find the general solution of the dierential equation
Solution. y (t) = k1 e5t +