1. Consider the differential equation
y+5y+4y :0.
a) (4 points) Find a fundamental set of solutions.
Answer: The Characteristic polynomial is p (A) = l2 + 5)» + 4 = (A + 1) (it + 4). The Characterisitic
roots are 1 and 4, so the functions
I 41
371(1): 6 a
Instructions: Number your answer sheets Erorn 1 to 4. Fill out all information at the top of
each sheet. D0 problem 71 on sheet n, n = 1, 2, 3,4. SHOW ALL WORK. Use both sides
of the sheet if necoessary. Please write out and sign the Honor Pledge on page
CLASS IIMI: DUI: Monday, September 'I b, 2006
Use algebraic techniques to evaluate the following limits. If a limit does not exist, write does not exist
because. followed by a clear & concise explanation. Your work must justify your results.
x24x+
(4): Be aware of possible typographical errors.
(1) The style of the nal exam will be similar to the practice.
(2) The following table Will be on the nal exam.
(3) For more practice problems, see midterm practice problems and exams.
1. (40 points) Determine Whether the following series converge or diverge. If a series
converges, nd its sum. Justify your answers and state all convergence tests used.
(a>Z<1m/§+
n:1
Solution. The series diverges by the n-th term test for divergence, si
Math 567 Notes
Differential equations: One independent variable, one or more dependent variables. In a
differential equation, we prescribe the rate of change of each dependent variable as a
function of given values of all the dependent and independent var
(1) Give the interval of existence for the solution of the initialvalue problem
d33: cos(3t) d2: 627:
1 = 2:2=2=0.
dt3 4itdt 1+t TU 5) M)
Solution. The coefcient and forcing are both continuous over the interval (*17 4),
which contains the initial time
Review Sheet for Math 1205 Test3
Test 2 covers sections 3.8, 3.10, 3.11, 4.1, 4.2, 4.3, 4.5 and MatLab worksheets 78
1. Differentiate the following:
sin2(x4) ' \h :\r\
. ,=]n-9
a y ( 3x3+1cI ) Us
2. A ladder 26 ft long rests against a vertical wall. If th