MATH 308, Spring 2016
Take Home QUIZ # 4
Due: Thursday 02 / 18 / 2016. In Class.
Print name (LAST, First):
SECTION #:
INSTRUCTOR: Dr. Marco A. Roque Sol
THE AGGIE CODE OF HONOR
"An Aggie does not lie, cheat, or steal, or tolerate those who do." By signing below, you indicate that all
work is your own and that you have neither given nor received help from any external sources.
SIGNATURE:
1. (10 pts.) Find the solution of
dy
= 6e2t−y ,
dt
.
y(0) = 0
2. (10 pts.) Find the solution of
(1 + t)
.
dy
+ y = cos(t),
dt
y(0) = 1
3. (10 pts ) Find the general ( implicit or explicit) solution of
(6xy − y 3 )dx + (4y + 3x2 − 3xy 2 )dy = 0
.
4. (10 pts.) Find the general solutions to
y 00 + 6y 0 + 7y = 0
.
5. (10 pts.) Find the general solutions to
(x + tan−1 y)dx +
.
x+y
1 + y2
dy = 0
6. (10 pts.) Determine (without solving the problem) an interval in which the solution of the given initial value
problem is certain to exist.
(ln(t))y 0 + y = cot(t);
.
y(2) = 3
7. (10 pts.) A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt
enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an
expression in terms of γ for the amount of salt in the tank at any time t. Also nd the limiting amount of salt
in the tank as t → ∞.
8. (10 pts.) In the following ODE problem
dy
= −2
dt
tan−1 (y)
1 + y2
;
−∞ < y0 < ∞
.
Determine the critical (equilibrium) points, and classify each one asymptotically stable, unstable, or semistable.
Draw horizontal strips dividing the ty-plane, acordingly to the critical points.