Carolyn Ren
1/3
02/07/2013
UNIVERSITY OF WATERLOO
Department of Mechanical Engineering
ME 203 Ordinary Differential Equations
Due date: Friday, July 26th, at 4:30 PM. There will be a drop-off box outside of my office that
day and it will be taken away by
Assignment # 4
1. Nagal. Page 99
Q2 A brine solution of salt flows at a constant rate of 6L/min into a large tank that initially held 50L of
brine solution in which was dissolved 0.5 kg of salt. The solution inside the tank is kept well stirred
and flows
Assignment #2
1. Page 43: solve the equation or initial value problem
Q11:
dy sec 2 y
dx 1 x 2
Q12: x
Q17:
dv 1 4v 2
dx
3v
y ' x 3 (1 y ) , y 0 3
2. Page 74: using the method of transformation and substitution to solve the
following ODEs.
Q11.
( y 2 xy)dx
Assignment
#3
1. Determine whether the given equation is separable, linear, neither or
both
Nagal. Page 51
Q1.
dx
xt e x
dt
2
Q2. x
dy
sin x y 0
dx
t
Q3. 3t e
dy
y ln t
dt
Q4. (t 1)
2
Q5. 3r
Q6.
x
dy
yt y
dt
dr
3
d
dx 2
t x sin t
dt
2. Solve the fo
ME203 Assignment #5
1. Using the method of Reduction of Order to find the solution for the following problems. (some of the
problems have been modified):
(a) Page 173, Q1 : y y 0 assuming y ' 0
y 9 y 0 y (0) 1 y (0) 1
(b) Page 174, Q24:
y 16 y 0 y (0) 0 y
Carolyn Ren
1/1
June 5, 2007
ME 203 Assignment 6
1. Find a general solution for the given differential equation. Nagal page 167:
a) Q1 y ' + 5 y '+6 y = 0
b) Q5 z ' + z ' z = 0
c) Q11 4 w ' + 20 w'+25w = 0
2. Solve the given initial value problem, Nagal p
Carolyn Ren
1/3
July 26, 2012
ME 203 Assignment 10
1. Nagal page 405: Use the convolution theorem to find the inverse Laplace transform of the given
function.
s
1
,
Q9:
a) Q5:
2
2
s s 1
s2 1
2. Nagal page 406: Q29
The current I t in an LRC circuit with vo
Carolyn Ren
1/3
July 17, 2013
ME 203 Assignment 9
1. Nagal page 359: Use Definition of the Laplace transform to determine the Laplace transform of the
following function
a) Q2 t 2
b) Q4 te 3t
2. Nagal page 359: Use the Laplace transform table and the line
Carolyn Ren
1/2
March 11, 2009
ME 203 Assignment 8
1. Nagal page 250: Q1
x'+ y ' = 2 y
a) Q1
x 2 y = y'
b) Q10
2 x'+ y ' x y = e t
x'+ y '+2 x + y = e t
Figure 2
2. Nagal page 251: Q31
Two large tanks, each holding 100 L of liquid, are interconnected by p