TEXAS A&M UNIVERSITY
DEPARTMENT OF MATHEMATICS
MATH 308
Exam 1 version A, 27 Sep 2013
On my honor, as an Aggie, I have neither given nor received unauthorized aid on this work.
Name (print):
No detailed analytical work — no points.
Each question is worth 5 points except for question 5.1
1.
Find the general solution of
x
dy
= 3y − 2x3 .
dx
2.
Find the general solution of
esin x + 2y
dy
+ yesin x cos x − 1 = 0.
dx
3.
Find the solution of
ex y 0 − y 2 sin x = 0,
y(0) = 1.
4.
A young person with no initial capital invests k dollars per year into equity with average
annualized return 7.5%. Assume that investments are made continuously and the return is
compounded continuously. Determine k so that $1 million is available for retirement in 40
years.
5.
For the equation
y 00 + 4y 0 + (6 + α)y = 0,
do only one of the following:
1. (for 3 points) Find the general solution for values of α = −4, −2, 2.
2. (for 5 points) Find the range of α for which the equation has at least one solution
which grows unbounded as t → ∞.
(You can attempt both part but you must indicate clearly which part you wish to submit
for grading; otherwise the minimum of two grades will be used)
Points:
/25