Math 244

Math 244:F7 Exam 0 Rutgers University, Dr. Molnar, July 8 2021 This is a 40-minute exam, with a five-minute grace period. You have until 3:15 to upload your solutions to Canvas. Please do not wait until the last minute. This exam is, by default, “open book”. This should be interpreted just as it would be if we were having our exam in the classroom. Specifically, you can consult your class notes, the notes that I have typed up for online classes, and the textbook, including solutions. No resources other than what I have listed above are allowed. You may not communicate with any other person regarding this exam, directly or indirectly. No computational assistance is allowed. This includes – but is not limited to – calculators, wolframalpha, Sage, Ramanujan, and an abacus. You need to do, and show, all the work. Answers given without justification will not receive full credit. Solutions must use techniques discussed so far in this course. Question Points 1 12 2 16 3 16 Total: 44 (This mini-exam counts out of 40 points.) Score Cover Page Print out this page, or write the honor pledge below, on a blank piece of paper, and sign. Place your photo ID (Rutgers ID preferred) on this page when photographing. Include this page as the first page of your pdf of the exam. Name: I hereby swear/affirm that I have neither given nor received any help on this exam, of any kind, to/from any source. Signature: Math 244 Midterm 0 Page 3 of 5 ty i s r e v s Uni dy 1. [12 points] Consider the DE “ y 4 ´ 2y 2 ` 1. Find and classify all equilibrium solutions. dt Draw the phase line, and sketch a representative selection of solution curves. er g t u ,R r a n l o M d i v a D 1 2 © 20 Math 244 Midterm 0 Page 4 of 5 2. [16 points] Solve the IVP p2x ` 18q ers g t u r, R a n l o id M © v a D 1 202 ty i s r e v Uni dy “ 3y ` x ` 9; yp0q “ ´5. dx Math 244 Midterm 0 Page 5 of 5 ty i s r e v Uni 3. [16 points] Gru recruits 4 minions per day to join his army. Unfortunately for him, each week, a quarter of his minions leave to get jobs at Starbucks, because they offer dental insurance. Currently, Gru has 4 minions, but if he reaches 100 minions, he will get to be on the front cover of Evil Overlord Monthly. Will this ever happen? If so, when? If not, why not? (You must set up and solve a differential equation.) ers g t u r, R a n l o id M © v a D 1 202
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