Math 308
Dierential Equations
Fall 2002
Homework 3 Solutions (Partial)
1(a). The right-hand side of the dierential equation is f (t, y ) = y/t, and this function is not continuous
at t = 0; in fact, it is not dened there. Also, f = 1 , which is also not c
Math 308
Dierential Equations
Fall 2002
Homework 2 Solutions
1 & 2.
See the last page.
3(a). Newtons second law of motion says that ma = F , and we know a = dv , so we have m dv = F . One
dt
dt
part of the force is gravity, mg . However, we are using the
Math 308
Dierential Equations
Fall 2002
Homework 1 Solutions
Text Problems
1.1/4.
(a) The statement of the problem says t is time, but it does not specify the starting point. I will dene t
to be the number of years since 1939. Then the initial condition,
Math 308 - Dierential Equations
Fall 2002
Homework Assignment 11
Due Friday, December 13
1. Consider the nonlinear system
dx
= x(1 x y )
dt
dy
= y (3 2x y )
dt
(a) Find all the equilibrium points.
(b) Find the linearization at each equilibrium, classify t
Math 308 - Dierential Equations
Fall 2002
Homework Assignment 10
Due Friday, December 6
1. For each of the following second order dierential equations, (i) use the method of undetermined
coecients to nd the general solution, and then (ii) solve the initia
Math 308 - Dierential Equations
Fall 2002
Homework Assignment 9
Due Friday, November 22.
1. Consider the system
dY
1
= AY , where A =
1/2
dt
1/2
.
0
(a) Find the general solution.
(b) Sketch the phase portrait. Include the straight-line solutions, and a f
Math 308 - Dierential Equations
Fall 2002
Homework Assignment 7
Due Friday, November 1.
For Questions 1-4,
(a) Find the general solution to the system
dY
= AY .
dt
(b) Sketch the phase portrait. Include the straight line solutions, and sketch several addi
Math 308 - Dierential Equations
Fall 2002
Homework Assignment 4
Due Friday, October 4.
1. Consider the dierential equation
dy
= y (y 2 + y + 1).
dt
The equation contains a parameter .
You can use Maple to create the graphs in this problem (but you dont ha
Math 308 - Dierential Equations
Fall 2002
Homework Assignment 3
Due Friday, September 27.
1. Consider the initial value problem
y
dy
=
dt
t
(a) Determine the region in the (t, y ) plane where the Existence and Uniqueness Theorems
apply.
(b) Pick 16 or so
Math 308 - Dierential Equations
Fall 2002
Homework Assignment 2
Due Friday, September 20.
1. On the last page of this assignment are ve dierential equations for u(t), and ve slope elds. Match
the equation with the slope eld.
2. In each of the slope elds i