## Elementary Differential Equations I / Ordinary Differential Equations

UBC MATH 215/255, Sep-Dec 2014, Problem sets and Exams

 we ek Due date Assignments Solutions 1 2 3 Wed 0917 h1 h1s 4 Wed 0924 h2 Students of section 102 can skip the last two problems from §1.6 since we did not cover enough on 0917 lecture h2s 5 Wed 1001 midterm exam 1Practice: Fall 2009 mt1 and its solution (#1b is not covered; #3b uses integration factor mu(y)); Spring 2010 mt1 and its solution (#3 uses integration factor mu(y); #4 is for mt2) mt1s afternoon-mt1s 6 Wed 1008 h3 h3s 7 Wed 1015 h4 h4s 8 Wed 1022 h5 h5s 9 Wed 1029 h6 h6s 10 Wed 1105 midterm exam 2 Revised table of Laplace transform to be provided in the exam Practice: Fall 2009 mt2 and its solution; Spring 2010 mt2 and its solution mt2s afternoon-mt2s 11 Wed 1112 h7 h7s 12 Wed 1119 h8 h8s 13 Wed 1126 h9 h9s Mon 1215 final exam: Mon Dec. 15th at 3:30 pm, Student Recreation Centre Room 200A (Room A of SRC A-B-C) Revised table of Laplace transform to be provided in the exam: same as above Practice: Fall 2007 final and its solution; Fall 2009 final and its solution; Spring 2010 final and its solution all past exams

h8 and h9:
• For Ass8, I marked 3.4.8, 3.7.2, 3.7.104 and 3.5.101. I considered 5 points for each problem.
• For ass9, I marked 3.9.8 and 8.1.3. I considered 10 pointsfor this assignment, 4 points for 3.9.4 and 6 points for 8.1.3. For the problem 3.9.8, many students tried to find the general solution, but you just asked them to check if the given vectors were solutions. So they did the harder work.
h7:
• I marked problems 6.3.4 , 6.3.8, 6.4.1 and 3.3.104. Most students solved the Assignment 6.3.4 as follows:
"It is the same as the previous problem (6.3.3):" and then they wrote the final answer.
This problem is not exactly similar to 6.3.3. Their final answers are different and so you were supposed to write clearly all steps.
h6:
• For h6, I marked the following problems: 6.1.12 , 6.1.13, 6.2.6, 6.2.8.
h5:
• I marked the problems 2.5.9 , 2.5.101, 2.6.3. , 2.6.101.
h4:
• I have marked questions 2.2.105, 2.4.2, 2.5.2 and 2.5.102.
h3:
• I chose, randomly, the exercises 1.6.6, 1.7.5, 2.1.7, 2.2.7.
• There is one paper with no name, also a student has done Assignment 2 that I didn't mark.
h2:
• I marked 1.4.102, Ex 6, Ex 14, Ex 18. Marks for each problem:
1.4.102: 5     Ex 6: 7     Ex 14: 4     Ex. 18: 4
So the total is: 20
• It seems we can solve the Exercise 18 of Braun in two ways, depending on what we consider as "integrating factor". The solutions we have put online is f(t)=t/2 + c/t , making the equation exact after multiplying the factor. However, the equation can be also solved as a linear equation, and we can then get f(t)=t . Both solutions were considered correct.
• Note that , for example in Ex 14, \phi(t,y)=(y^2 *e^t)/2 - y*e^(2t)+c is not a solution for the given differential equation. The correct solution should be given as \phi(t,y)=(y^2 *e^t)/2 - y*e^(2t)+c =0
• Try to do the assignment by yourself. Discussions are encouraged, but after you have thought about problems by yourself. At the end, you should write the solutions by yourself alone and you need to understand them fully. I see that some people has just copied from each other. This is not gonna help you for your exam.
h1:
• I marked the problems 1.1.4 , 1.2.3 , 1.2.103 , 1.3.4.
• most people just copied the solutions from others
• 1.1.4: Most people didn't remove or didn't know how to remove |(x-1)/(1+x)| = (1-x)/(1+x). But they did it in question 1.3.4 (or maybe didn't know they had to put an absolute value in ln after integrating)
• 1.2.103. Most people tried to integrate and analyse the solution they got (which is not what you wanted; it is not correct) some people said f(x,y) is not continuous, but indeed it is not defined at (x,y)=(1,2).