Math 307E/H Final Exam
Practice Problems
1. Find the general solution to each of the following dierential equations
by any method. It is acceptable to leave the answer in implicit form
when necessary.
(a) y 2y = t2 e2t
Solution: y =
t3 2 t
3e
+ Ce2t
(b) y
Math 307E/H Final Exam
Practice Problems
1. Find the general solution to each of the following dierential equations
by any method. It is acceptable to leave the answer in implicit form
when necessary.
(a) y 2y = t2 e2t
(b) y + 2y 8y = 0
(c) y y y = tet
(d
Math 307E/H Midterm Exam 1
Practice Problems
Below is a selection of practice problems for your upcoming midterm. Please
note: A true exam would have only 4-5 problems. These exercises are intended
as a guide to what kinds of things to expect on the exam,
Math 307E/H Midterm Exam 1
Practice Problems Solutions
1. A tank contains G gallons of fresh water. A solution with a concentration of
m lb of salt per gallon is pumped into the tank at a rate of r gallons per
minute. The well-mixed solution drains from t
Math 307E/H Midterm 2
Practice Problems
1. Find the general solution to each of the following dierential equations:
(a)
(b)
(c)
(d)
y
y
y
y
+ y 2y = 2t
+ 4 y = t2 + 3 et
+ 2y + y = et
+ 4y = 3sin(2t)
t
e
(e) y 2y + y = 1+t2
(f) y + y = tan t
(g) t2 y + 3t
Math 307E/H Midterm 2
Practice Problems Solutions
1. Find the general solution to each of the following dierential equations:
(a) y + y 2y = 2t
We rst solve the corresponding homogeneous equation y + y 2y = 0. Using
the characteristic equation, we obtain
Math 307 I - Spring 2011
Final Exam
June 07, 2011
Student number:
Name:
1
2
3
4
5
6
7
8
9
10
Total
10
10
10
10
10
10
10
10
10
3*
90
Complete all questions.
You may use a scientic calculator during this examination. Other electronic devices (e.g.
cell ph
Midterm 1 Solutions
Math 307 Winter 17
January 30, 2017
Problem 1. For each of the following initial value problems, find the explicit solution and describe the
limiting behavior of the solution.
(a) y 0 = 3y + 2et ,
y(0) = 2
(i) Solve the initial value p