m05x2f09 - Math 205 Second Exam N AM E Section(Last First...

Math 205 Second Exam October 29, 2009
NAME : Section
(Last, First)
LECTURE :
Prof. Skandera (MWF 9am, Sect. 10)
Prof. Dodson (MWF 11am, Sect. 11)
Prof. Dodson (MWF 3pm, Sect. 12)
Prof. Zhang (TuTh 10:45 am, Sect. 13)
Question 1: /20
Question 2: /20
Question 3: /15
Question 4: /25
Question 5: /20
Total: /100
Instructions : This is a 60 minute exam. You are not to have or use a calculator
during the exam. You will be graded on the work shown on your paper; an answer
without the correct supporting steps may receive no credit. Solutions to differential
equations are not to include integrals; and must be expressed only in terms of real
numbers and real functions.

1. In this problem, solutions to differential equations are not to include integrals.
(a) (10 points ) Solve the differential equation ( x 2 + 1)
dy
dx
= xy and write your
solution as an explicit function y = y ( x ) .
(b) (10 points ) Solve the differential equation
dy
dx
+
1
1 - x
¶
y =
√
1 - x, then
solve the initial value problem y (0) = 1 .

2. (20 points ) Find the general solution of the following differential equations. In