MATH 308 Midterm: MATH 308 TAMU Exam1
Document Summary
Math 308 sections 509 & 510 di erential equations. No personal aids or calculators are permitted: if you require more space to write your answer, you may continue on the back of the current page. There is also a blank page at the end of the exam: explain your work! Little or no points will be given for a correct answer with no explanation of how you got it. If you use a theorem to answer a question, indicate which theorem you are using, and explain why the hypotheses of the theorem are valid: good luck! Explain why/why not! (a) (5 points) dy dx = x ln y + y; y(1) = 1. Solution: let f (x, y) = x ln y + y. Then f is continuous on a rectangle around (0, 0), Thus the existence-uniqueness theorem shows that however fy = 1 solutions exist, but may not be unique.
