MATH 325 Midterm: MATH325 Fall 2010 Exam

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 325
• Professor: All

Document Summary

Instructions: answer all questions in the exam booklets provided. Start each question on a new page: all questions carry equal weight, this is a closed book exam. No crib sheets, textbooks or any other aids are permitted: calculators are permitted, dictionaries are not permitted. This exam comprises the cover page, 2 pages of 6 questions and a table of laplace. 1. (a) solve (implicitly) (3x2y + 2xy + y3)dx + (x2 + y2)dy = 0, by nding an integrating factor (x) (which is a function of x only). (b) find the general solution y(x) of. 2. (a) let y(4) 3y 4y = x + e2x. y (t) = y(t)2 3, y(0) = 2, and let y0(t) = 2 for all t > 0. Show that there is a unique choice of c1, c2 such that y(x) = c1y1(x) + c2y2(x) + yp(x) solves the initial value problem.