Written Assignment #1: Due Monday, June 11
1. Classify each of the following according to order and linearity:
a. 1 ln 15 tan5
b. cos
c. 5 13 cos tan
2. For each of the following initial value problems:
i.
Verify that the given function represents a fami

Differential Equations
Take-home Exam 2
Summer 2013
Due Monday, July 15 at 11:59 pm
Directlons: Show your work whenever possible for maximum credit. A correct answer is worth
one point; the remaining points are for the supporting work.
[1] Flnd the gene

Written Assignment #5
Section 4.6 Variation of Parameters
Solve each of the following problems using Variation of Parameters.
1. 2 sin
2. 9 csc 3
Section 4.7 Cauchy-Euler Equations
Solve each of the following differential equations. Use the substitutio

A large tank is filled to capacity with 500 gallons of pure water. Brine containing 2
pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. The wellmixed solution is pumped out at the same rate.
a) Draw a picture of the situation, clea

A torpedo is traveling at a speed of 60 miles/hour at the moment it runs out of fuel. If
the water resists its motion with a force proportional to the speed, and if 1 mile
of travel reduces its speed to 30 miles/hour, how far will it coast?
Hints:
Based

The equation
2 + + = 0,
where p and q are constants, is known as Eulers equidimensional equation. 1
Show that if one makes the change of independent variable = , then
1
1
(a)
= (so = ), and
2
2
1
(b)
= 2 2 .
2
(c)
Conclude that this change of variab