final2007

final2007 - Final Exam MATH 150: Introduction to Ordinary...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Final Exam MATH 150: Introduction to Ordinary Differential Equations J. R. Chasnov 13 December 2007 Answer ALL questions Full mark: 80; each question carries 10 marks. Time allowed – 2 hours Directions – This is a closed book exam. You may write on the front and back of the exam papers. Student Name: Student Number: To solve y ′ + p ( x ) y = g ( x ) , y ( x ) = y , let μ = exp ( integraltext x x pdx ). Then, y = 1 μ ( y + integraltext x x μgdx ). Question No. (mark) Marks 1 (10) 2 (10) 3 (10) 4 (10) 5 (10) 6 (10) 7 (10) 8 (10) Total Question 1 Score: (a) (8 pts) Find the solution of the following ode for y = y ( x ) that passes through the origin ( y (0) = 0): e x − y y ′ + e y − x = 0 . (b) (2 pts) For what values of x does the solution exist? Question 2 Score: (a) (8 pts) Find the solution y = y ( x ) with x > 0 of xy ′ + (1 + x ) y = xe − x , y (1) = 0 . (b) (2 pts) Find the cubic equation whose positive root is the value of x at which y ( x ) is maximum. Question 3...
View Full Document

This note was uploaded on 01/28/2011 for the course MATH 150 taught by Professor T.qian during the Spring '09 term at HKUST.

Page1 / 9

final2007 - Final Exam MATH 150: Introduction to Ordinary...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online