MATH 2120, Homework 5
1. Find the general solution to the system x0 = Ax, where A is as specified below. Make sure to write
the solution in purely real form.
1 0
(a) A =
.
4 3
1
Answer. The two eige
MATH 2120 Quiz 2
Tuesday October 7, 2014
1. For the rst order ODE
(3t + y) y = t 2y ,
make the substitution v(t) = y(t)/t to obtain a separable equation for v(t). Write the equation for v in the form
MATH 2120 Quiz 1
1.
Thursday September 25, 2014
(a) Find the solution of the initial value problem
2
dy
y = et/3 ,
dt
y(0) = a .
(b) There exists a critical value a0 for which a < a0 and a > a0 produ
MATH 212% - Qiiiz l Thursday September 25, 29M
l. (a) Find the solution of the initial value problem
d?! 15/3
z 0:.
2dt 2; e , y() a
(b) There exists a critical value a0 for which a < a0 and a > (t
Math 2120
Final Exam
Saturday, December 12, 2015
Answer the questions in the space provided on the question sheet.
A basic calculator is allowed.
The test will run from 8:30-11:30.
The included ex
1.2.3
Exercises
Exercise 1.2.1: Sketch slope field for y0 = e x y . How do the solutions behave as x grows? Can you
guess a particular solution by looking at the slope field?
Exercise 1.2.2: Sketch
sl
MATH 2120, Homework 7
1. A two-mass, three-spring system consists of two masses at positions (x (t) , y(t) attached by a
spring to each other and to two adjacent walls. An example of such a system (wi
MATH 2120, Homework 3
1. Consider the differential equation y 0 (t) = y(y1)(y2). (a) Draw the phase diagram, find all steady
states, and classify the critical points stable or unstable. (b) Find lim y
MATH 2120, Homework 2
1. Consider a pond that initially contains 10 million gal of fresh water. Water containing an undesirable chemical flows into the pond at the rate of 5 million gal/yr, and the mi
MATH 2120, Homework 1
dy
= x2 + 1 subject to initial condition y(1) = 2. What is y(3)?
dx
Answer. Integrating we have
Z
y(x) =
x2 + 1 dx
1. (1.1) Solve
=
x3
+x+C
3
for some constant C. Plugging in x =
MATH 2120, Homework 4
1. (a) Write down a second order linear ODE that has the following particular solutions: y1 = ex , y2 =
e2x .
Answer. The exponents are 1, 2 so that the characteristic equation i
Practice questions for midterm
1. Review all the homework questions (up to and including hw4).
2. Solve the following first-order ODEs.
y
2x
2y = 3e 3x , y(0) = 3
(a) y 0 =
(b) y 0
(c) 2x y 0
y = 2x1/
MATH 2120, Homework 3
1. Consider the dierential equation y 0 (t) = y(y 1)(y 2). (a) Draw the phase diagram, find all
steady states, and classify the critical points stable or unstable. (b) Find lim y
MATH 2120, Homework 4
1. (a) Write down a second order linear ODE that has the following particular solutions: y1 = ex , y2 =
e2x .
(b) Write down a second order linear ODE with real coefficients that
MATH 2120, Homework 6
1. Compute eAt where A is one of the following matrices.
1 2
(a) A =
2 1
1 1
(b) A =
2 1
1 1
(c) A =
1 3
1 0 0
(d) A = 0 1 2
0 2 1
2. (a) Find the general solution to ~x0 = A~x
MATH 2120, Homework 5
1. Find the general solution to the system x0 = Ax, where A is as specified below. Make sure to write
the solution in purely real form.
1 0
(a) A =
.
4 3
1 5
(b) A =
.
1 3
1
0 0
MATH 2L2A, Homework
1.
2.
3
Consider the difierential equation A'(t) : A(A - l)(V - Z) (u) Draw the phase diagra,m, fintl all
steady states, and classi$, the critical points stable or unstable. (b) Fi
Review/practice questions final exam
Topics covered:
First-order ODEs:
Solving: separable, linear (nonhomogeneous), exact, integrating factors
Mixing problems, Newtons law of cooling
Linear ODEs:
Practice questions for midterm
1. Review all the homework questions (up to and including hw4).
2. Solve the following first-order ODE's.
,/, a',:
u
\a)
2,
:3e-3", g(0) : 3
(c) 2* yt - A :2*'/', y(7) :
Homework on Laplace Transorms
1. Find Laplace transforms of the following functions (Note: you should use Laplace transforms table,
no integration required!):
(a) f (t) = sin(t) exp(2t)
(b) f (t) = si
Math 2120
Test 1
Monday, May 16, 2016
You only need something to write with. No formula sheets of any kind.
If I suspect you of cheating you will have your test taken from you.
Make sure there is a
Sample Math 2120 nal exam from 2009.
You have 3 hours to complete this exam. No calculators or cheatsheets allowed
A table of Laplace transforms is provided.
There are 7 questions, including a bonus q