Xyllene Guerra
Assignment math215255WW5 due 02/22/2016 at 09:00am PST
MATH215-255-ALL 2015W2
year
1946
USSR (x)
14
US (y)
80
1. (1 pt) Write the system x 0 = e9t x 3ty + 6 sin(t), y 0 =
7 tan(t) y + 6x 9 cos(t) in the form
d x
x
= P(t)
+ ~f (t).
y
dt
MATH 215S - MIDTERM I - SOLUTION KEY
Problem I. Short answer questions. In general if the correct answer is anywhere on the page give
the full points. For two point question only check if the correct answer is given, otherwise 0 point.
For 3 point questio
MATH 215S - PRACTICE MIDTERM
Problem I. (18 points) Short answer questions. Here you only need to give the correct answer no
detailed explanations/ calculations are needed to support your answer.
(a) (2 points) Find a solution of the form y = tr of the eq
Midterm 2
1. Find the general solution to the following inhomogeneous linear system
t
2
e
~x(t) +
1
0
0
~x (t) =
1
0
Solution: ~xgen (t) = ~xhom (t) + ~xpart (t).
First find the solution to the homogeneous equation: the characteristic equation
is ( + 1)
MATH 255: Project 2, due date: April 3
Content : 3 problems, Total mark: 3 points
This is a team project. You can submit this project in a group of two.
Problem 1: Two-mass, three-spring system
Consider the two-mass, three-spring system we discussed in cl
MATH 255: Project 1, due date: February 27
Content : 2 problems, Total mark: 2 points
This is a team project. You can submit this project in a group of two.
Problem 1: Heating of a building
Time variation of temperature inside a building can be modelled u
Math 215/255 Practice Midterm 1
1. (10 marks) Consider the following initial value problem, where a, b, c are given constants:
ax + by
dy
=
,
dx
bx + cy
y(a) = c.
a. For what values of a, b, c is the differential equation non-linear?
b. Find the solution
MATH 215 — section 201 : Quiz 2, February 24 2016
Duration : 15 minutes. No lecture notes, no textbooks, no calculators.
Content : 2 problems, Total : 25 points
Write clearly your final answer in the box for each question. Only the answers written in the
MATH 215/255
Fall 2014
Assignment 6
6.1, 6.2
Solutions to selected exercises can be found in [Lebl], starting from page 303.
6.1.8: Find the Laplace transform of cos2 (t).
1
Answer. As follows from trigonometric identities, cos2 (t) = 2 (1+cos(2t). Using
MATH 215/255
Fall 2014
Assignment 4
2.2, 2.4, 2.5
Solutions to selected exercises can be found in [Lebl], starting from page 303.
2.2.9: Solve y + 9y = 0 for y(0) = 1, y (0) = 1.
Answer.
The characteristic equation of y + 9y = 0 is:
r2 + 9r = 0.
Solve r2
MATH 215/255
Fall 2014
Assignment 5
2.5, 2.6
Solutions to selected exercises can be found in [Lebl], starting from page 303.
2.5.7: a) Find a particular solution of y 2y + y = ex using the method of variation
of parameters.
b) Find a particular solution
MATH 215/255
Fall 2014
Assignment 1
1.1, 1.2, 1.3
Solutions to selected exercises can be found in [Lebl], starting from page 303.
1.1.3: Solve
dy
= sin(5x), for y(0) = 2.
dx
Answer.
1
sin(5x)dx = cos(5x) + c.
5
y=
Using y(0) = 2, we have 2 = 1 + c and he
MATH 215/255
Fall 2014
Assignment 3 solutions
1.6, 1.7, 2.1, 2.2
Solutions to selected exercises can be found in [Lebl], starting from page 303.
1.6.6: Start with the logistic equation dx = kx(M x). Suppose that we modify our
dt
harvesting. That is we wi
MATH 215/255
Fall 2014
Assignment 8
due 11/19
3.4, 3.7, 3.5, 3.9
Solutions to selected exercises can be found in [Lebl], starting from page 303.
3.4.6: a) Find the general solution of x1 = 2x1 , x2 = 3x2 using the eigenvalue method
(rst write the system
MATH 215/255
Fall 2014
Assignment 9
3.9, 8.1, 8.2
Solutions to selected exercises can be found at the end of the draft chapter of Lebls book
on nonlinear systems.
3.9.8: Consider the equation
=
x
1/t 1
1 1/t
+
x
t2
t
+ c2
t cos t
t sin t
.
Check that a
MATH 215/255
Fall 2014
Assignment 7
6.3, 6.4, 3.1, 3.3
Solutions to selected exercises can be found in [Lebl], starting from page 303.
6.3.3: Find the solution to
mx + cx + kx = f (t), x(0) = 0, x (0) = 0
for an arbitrary function f (t), where m > 0, c >