Math 232 (Winter 2007) Assignment #5
Q1. Industrial waste is pumped into a tank containing 1000 gallons of water at the
rate of 1 gal/min, and the well-stirred solution leaves the tank at the same rate. (a)
Find the concentration of waste in the tank at t
Math 232 (Winter 2007) Assignment #4
Q1. The initial mass of a species of sh in a lake is 7 million tonnes. The mass of sh,
if left alone, would increase at a rate proportional to the mass, with a proportionality
constant of 2/year. However, commercial sh
Student Number
Student Name (Printed)
Page 1 of 7
QUEENS UNIVERSITY
MATH/MTHE 232 Midterm Test #2
Friday, 21 March, 2014
INSTRUCTIONS
This test is 50 MINUTES in length and consists of 4 questions.
Answer all questions, writing clearly in the space provi
Practice problems for MATH/MTHE 232
April 10, 2014
1
Problems
1. Determine whether or not the following functions are solutions to the given dierential equations.
(a) y = 3x2 ,
y(x) = x3 + 5
(b) y = 9y,
y(x) = sin(3x)
y(x) = ex cos(x)
2
(d) y + 2xy 2 = 0,
Student Number
Student Name (Printed)
Page 1 of 6
QUEENS UNIVERSITY
MATH/MTHE 232 Midterm Test #1
Thursday, 13 February, 2014
INSTRUCTIONS
This test is 50 MINUTES in length and consists of 5 questions.
Answer all questions, writing clearly in the space
Practice problems for MATH/MTHE 232
March 20, 2014
1. Find the general solution to the following systems of dierential equations.
(a)
x
y
=
0 1
4 2
(b)
x
y
=
3 3
2 2
(c)
x
y
=
0 1
1 2
(d)
x
y
=
5 2
2 1
x
y
x
y
x
y
x
y
2. For each of the systems in the pre
Math 232 (Winter 2007) Assignment #8
Q1. Let L[y](t) = y (t) 3ty (t) + 3y(t). Compute: (a) L[cos
3t], (b) L[2et + 4 cos
3t]
Solution: This is a straight-forward calculation.
(a) We have
L[cos
3t) 3t(cos 3t) + 3(cos 3t)
= 3 cos 3t + 3 3t sin 3t + 3 cos 3t