ME 203
Ordinary Differential Equations
Assignment 1
1. Fill in the following Table.
Differential Equation
y 4 y 5 y = e3 x
Ordinary
or Partial
Independent
Variables
Dependent
Variables Order
Linear or
Non-linear
U
2U U
=4 2 +
t
x
y
2
3
d 3s d 2 s
3 +
Question 1
similar to this
Question 2
Question 3
Question 4
Question 5 a)
Question 5 b)
Question 6 a)
Question 6 b)
Question 7
Question 8 a)
Question 8 b)
Question 8 c)
Fall 2014
Question 1
(a)
(b)
(c)
Question 2
Question 3
(a)
Please Note: Challenge questions involve
extensions past what is expected that you
know for the course.
(b)
(c)
Question 4
This is a challenge question to show that
there are many interconnected c
ME 203
Ordinary Dierential Equations
Assignment 2
Solutions to First Order ODEs
1. Solve each of the following, subject to conditions where given.
(a) 3x(y 2 + 1)dx + y(x2 + 2)dy = 0
(b) x 1 + y 2 dx = y 1 + x2 dy
(c) 2y cos(x)dx + 3 sin(x)dy = 0; y
2
=2
ME 203
Ordinary Dierential Equations
Assignment 6
Solution to Simultaneous Sets of ODEs
1. Find the solution of each system subject to any given conditions
(a)
(b)
d2 y
=x
dt2
dy
dt + 6y
2
x
2, d 2 = y + 2
dt
=
dx
dt , 3x
dx
dt
= 2 dy ; x = 2, y = 3 at t
ME 203
Ordinary Dierential Equations
Assignment 7
Laplace Transforms
1. Using the denition, nd the Laplace transform of each of the following functions. In each
case specify the values of s for which the transform exists. Compare with results obtained
fro
ME 203
ORDINARY DIFFERENTIAL EQUATIONS
Assignment 3
1) Oil is poured into the conical container shown on the attached diagram at a constant rate, Qi
cm3/s. The outflow is given by the equation
=
2
cm3/s, where c = 0.6, Ao is
exit area and g is gravitation
ME 203
Ordinary Dierential Equations
Assignment 5
Method of Undetermined Coe cients and Variation of Parameters
1. Using the characteristic/auxiliary equation write the general solutions to the problems:
16y 00
(a) y IV =
(b) U 00 (t) =
16U (t); U (0) = 0
ME 203
Ordinary Dierential Equations
Assignment 4
Reduction of Order: ODEs with and without Constant Coecients
Before the midterm:
1. Solve each of the following subject to conditions where indicated.
(a) x3 y = 1 +
x
(b) xy + 2y = 0
2. 1 + (y )2 + yy = 0