Graphing the First Order Differential Equations in Maple
Basic addition, subtraction, multiplication and division: +, -, * and /
Always restart each problem with: >restart:
1. Load the DEtools and plo
Test 1 Dierential Equations Solutions 2/15/02
Write your name on the back of your test. Show all work. Where possible test your solutions.
1.(10) Use the guess and test method to solve the second orde
Test 1 Dierential Equations 2/15/02
Write your name on the back of your test. Show all work. Where possible test your solutions.
1.(10) Use the guess and test method to solve the second order dierenti
Test 2 Dierential Equations Spring 2002, makeup due 4/22/02
Write your name on the back of your test. Show all work. You must check your work to receive credit.
1.(14) For the dierential equation
d2 y
Test 2 Dierential Equations Spring 2003, April 7-8, Solutions
Write your name on the back of your test. Show all work. Where possible test your solutions.
1.(25) For the dierential equation
d2 y
+ 10y
Quiz 3.4 Make up Solution, 3/26-3/31/03
1) Solve the 2-dimensional system of dierential equations
dY
dt
2
2
Y
13 4
=
1
.
1
Solution: First we nd the eigenvalues of the matrix:
with initial condition Y
Homework 1, Selected Problems
1.1 6. Suppose two students memorize lists according to the same model
dL
= 2(1 L).
dt
a) If one of the students knows one-half of the list at time t = 0 and the other kn
Practice Material for Final Dierential Equations
Note that this list of questions is not exhaustive. You should also be prepared to answer questions
such as those on test 1, test 2, the make up test f
Practice Material for Final Dierential Equations
Note that this list of questions is not exhaustive. You should also be prepared to answer questions
such as those on test 1, test 2, practice tests, in
Quiz 2 Dierential Equations Solutions
For the initial value problem:
dy
dt
=
1
, y (0) = 0
(y + 2)(t 1)
(a) Find a formula for the solution.
Solution: The dierential equation is separable, so we have
3.4 (b) Classification of Systems with
Complex Eigenvalues
Ei
Linear Combinations of Sines and Cosines
x(t ) = 3sin(2t ) + 4 cos(2t )
1
Amplitude and Phase
x(t ) = a sin t + b cos t , a > 0
Half
Half-
3.4 (a) Systems with Complex Eigenvalues
(a) Systems with Complex Eigenvalues
A System with Complex Eigenvalues
2 1
dY
= AY, A =
dt
5 4
Eigenvalues :
2
det
5
1
2
= (2 )(4 ) + 5 = 6 + 13
4
2 6
3.3 Systems with Real Eigenvalues
A Diagonal System
dx
= 3x
3 0 dt
dY
= AY, A =
:
dy
dt
0 2
= 2y
dt
1
1 = 3, V1 =
0
Eigenvalues and eigenvectors :
= 2, V = 0
2
2
1
1
0 k e 3t
General Solution
3.1 Properties of Linear Systems
Properties of Linear Systems
Linear Systems
Pauls Rock and Roll CDs & Bobs Opera Only Discs:
x(t ) = daily profit of Paul's store
y (t ) = daily profit of Bob's store
8/21/2012
3.2 Straight-Line Solutions
Straight
Solutions
The Plan
dx
= ax + by
dt
dy
= cx + dy
dt
a b
dY
= AY, A=
dt
c d
1) Find two linearly independent solutions Y1 (t), Y2 (t)
2) Use the principle
Test 2 Dierential Equations Spring 2002, makeup due 4/22/02
Write your name on the back of your test. Show all work. You must check your work to receive credit.
1.(14) For the dierential equation
dy
d