## Math 251## Ordinary and Partial Differential Equations## Sample Exams |

- Exam I, Spring 1998
- Exam I, Spring 2000
answer key
- Exam I, Fall 2000
answer key

*Question 6 on this exam is among the trickiest application problems to appear on a Math 251 exam in the past decade... It is not quite the mixing problem as given in the textbook, but with a slight twist. You'll need to think a little to come up with the correct model/initial value problem.* - Exam I, Fall 2001
answer key

*The graphs are missing from question 6b. You can ignore the part, or sketch the correct direction field yourself.* - Exam I, Spring 2002
answer key and complete solutions
- Exam I, Summer 2002
answer key
- Exam I, Fall 2002
answer key and complete solutions
- Exam I, Spring 2003
answer key
- Exam I, Summer 2003
answer key
- Exam I, Fall 2003
answer key
- Exam I, Spring 2004
answer key
- Exam I, Fall 2004
answer key
- Exam I, Spring 2005
answer/grading key and solutions
- Exam I, Fall 2005 (questions and answer key) - Professor Glasner's sections
- Exam I, Fall 2005 - common exam for other sections
questions and answer/grading key
- Exam I, Summer 2006
answer key
- Exam I, Spring 2007
answer key
- Exam I, Summer 2007
answer key
- Exam I, Fall 2007
answer key
- Exam I, Spring 2008
answer key
- Exam I, Summer 2008
answer key
- Exam I, Fall 2008
answer key
- Exam I, Spring 2009
answer key
- (Math 251H Honors section) Mock/Practice Exam I, Spring 2009
- Exam I, Summer 2009
answer key

*There was only one midterm exam during the Summer semester, 2009. This is that exam. It covers up to section 6.2.* - Exam I, Fall 2009
- Exam I, Spring 2010
answer key
- Exam I, Summer 2010
answer key
- Exam I, Fall 2010
answer key
- Exam I, Spring 2011
answer key
- Exam I, Summer 2011
answer key
- Exam I, Fall 2011
answer key
- Exam I, Spring 2012
answer/grading key
- Exam I, Summer 2012
answer key
- Exam I, Fall 2012
answer key
- Exam I, Spring 2013
answer key
- Exam I, Summer 2013
- Exam I, Fall 2013
answer/grading key and complete solutions
- Exam I, Spring 2014
answer key and solution
- Exam I, Summer 2014
- Exam I, Fall 2014
answer key
- Exam I, Spring 2015
answer key
- Exam I, Summer 2015
answer key
- Exam I, Fall 2015
- Exam I, Spring 2016
answer key
- (Math 251H Honors section) Exam I, Spring 2016
answer key and solutions
- Exam I, Summer 2016
answer key
- Exam I, Fall 2016
- Exam I, Spring 2017
- Exam I, Fall 2017
answer key and solution

- Exam II, Spring 2000
- Exam II, Fall 2000
answer key
- Exam II, Fall 2001
- Exam II, Summer 2002
answer key
- Exam II, Fall 2002
answer key
- Exam II, Spring 2003
answer key

*It says Exam 1 on the cover, but it is indeed the second exam.* - Exam II, Summer 2003
answer key
- Exam II, Fall 2003
answer/grading key and complete solutions (very detailed).

*Due to an error in putting together the exam package, the table of Laplace transforms was unavailable to students taking the conflict exam. Therefore, a separate set of Laplace transform problems was made as a mini re-test and given to the affected students as a remedy. Here is the Laplace re-test.*

Exam II Laplace transforms make-up test, Fall 2003 answer key and complete solutions - Exam II, Spring 2004
answer key
- Exam II, Spring 2005
answer key
- Exam II, Fall 2005 (questions and answer key) - Professor Glasner's sections
- Exam II, Fall 2005 (questions and answer/grading key) - common exam for other sections
- Exam II, Summer 2006
answer key
- Exam II, Spring 2007
- Exam II, Summer 2007
answer key
- Exam II, Fall 2007
answer key
- Exam II, Spring 2008
answer key
- Exam II, Summer 2008
answer key
- Exam II, Fall 2008
answer/grading key (interim).

*This was a draft version of the grading key - there was a mistake in #12 (the correct answer is y(t)=e^{-3t} + u(t-2)(5/9+(t-2)/3-5/9 e^{-3(t-2)}) + u(t-3)e^{-3(t-3)}); in addition, also acceptable as an answer to #2(a) was "none", since the eigenvectors do not match what's given in the saddle point phase portrait.* - Exam II, Spring 2009
answer key
- (Math 251H Honors section) Mock/Practice Exam II, Spring 2009
answer key
- There was not a second midterm exam during the summer 2009 semester, only the exam I and final exam.
- Exam II, Fall 2009
- Exam II, Spring 2010
- Exam II, Summer 2010
answer key
- Exam II, Fall 2010
answer key
- Exam II, Spring 2011
answer key
- Exam II, Summer 2011
answer key
- Exam II, Fall 2011
answer/grading key
- Exam II, Spring 2012
answer key
- Exam II, Summer 2012
answer key
- Exam II, Fall 2012
answer key
- Exam II, Spring 2013
answer key
- Exam II, Summer 2013
answer key and complete solutions
- Exam II, Fall 2013
answer/grading key
- Exam II, Spring 2014
answer key
- Exam II, Summer 2014
answer key
- Exam II, Fall 2014
answer key

*The missing answer at the very end is: #12(c) "saddle point, unstable".* - Exam II, Spring 2015
answer key
- Exam II, Summer 2015
answer key
- Exam II, Fall 2015
answer key and solutions
- (Math 251H Honors section) Exam II, Spring 2016
answer key and solutions
- Exam II, Spring 2016
answer key
- Exam II, Summer 2016
- Exam II, Fall 2016
- Exam II, Spring 2017
answer key

- Final Exam, Fall 1999
- Final Exam, Spring 2000
- Final Exam, Fall 2000
answer key
- Final Exam, Fall 2001
- Final Exam, Summer 2002
- Final Exam, Spring 2003
answer key
- Final Exam, Summer 2003
answer key
- Final Exam, Fall 2003
answer key
- Final Exam, Spring 2004
answer key
- Final Exam, Spring 2005 (questions and answer key)
- Final Exam, Fall 2005 - Professor Glasner's sections
- Final Exam, Fall 2005 - common exam for other sections
questions and answer/grading key
- Final Exam, Spring 2007
answer key
complete solution (detailed)
- Final Exam, Fall 2007
answer key
- Final Exam, Spring 2008
answer key
- Final Exam, Fall 2008
answer key
- Final Exam, Spring 2009
answer key
- (Math 251H Honors section) Mock/Practice Final Exam (version 1), Spring 2008/2009
- (Math 251H Honors section) Mock/Practice Final Exam (version 2), Spring 2008/2009
- Final Exam, Summer 2009
answer key

*This exam is shorter and simpler than usual. It is not a typical representative of the comprehensive final exams like the others.* - Final Exam, Fall 2009
- Final Exam, Spring 2010
answer key
- Final Exam, Summer 2010
answer key
- Final Exam, Fall 2010
answer key
- Final Exam, Spring 2011
answer/grading key
- Final Exam, Summer 2011
answer key
- Final Exam, Fall 2011
answer key
- Final Exam, Spring 2012
answer/grading key
- Final Exam, Summer 2012
- Final Exam, Fall 2012
answer key
- Final Exam, Spring 2013
answer/grading key and complete solutions
- Final Exam, Summer 2013
- Final Exam, Fall 2013
answer/grading key and complete solutions
- Final Exam, Spring 2014
answer/grading key and complete solutions
- Final Exam, Summer 2014
- Final Exam, Fall 2014
answer key
- Final Exam, Spring 2015
answer/grading key
- Final Exam, Summer 2015
- Final Exam, Fall 2015
answer/grading key and complete solutions
- Final Exam, Spring 2016
answer/grading key and complete solutions
- Final Exam, Summer 2016
- Final Exam, Fall 2016
- Final Exam, Spring 2017
answer/grading key and complete solutions

*The correct answer to 16(c) should be "true" since the case h(x) = j(x) = 0 is not ruled out by the question, in fact in part 16(d) it is explicitly stated that either function could be 0.*

Additional sample problems can be found here: Math 250 Sample Exams Page

Send any question/comment about this page to: tseng@math.psu.edu

*Last modified: October 30, 2017*