MATH 202 Exam 1, Spring 2004

MATHEMATICS 202 SPRING SEMESTER 2004 QUIZ I Instructors: Ms. 8. Jaafar, Dr. Abdallah Lyzzaik, Dr. Husam Yamani Date: March 18, 2004 Time: 60 MINUTES Answer the following five questions: 1. Solve the initial-value problem (10 points) (e+ 2y+1)dx —-(2e+4y+8)dy=0, y(0)=~1. 2. Solve the differential equation (10 points) d ro =y~xeos* (2), zr>0. dz QL 3. Solve the initial-value problem (10 points) (2y —4zty*)\dr+a2dy=0, y(1) = 1/7. 4. Solve the differential equation (10 points) (y+y’cosz)dx + (2x+3ysinz)dy=0, y>O. 5. (a) State the existence and uniqueness theorem for the initial-value problem (4 points) d; = Flay), —y(vo) = wo. (b) Determine the largest region of the ry—plane for which the differential equation (6 points) dy _ lfzisy #5 (2+!) would have a unique solution whose graph passes through a point (xp, yo) in the region. Find, by inspection, the solution passing through any point (x, x), 2 #0.