=========================preview======================
(MATH150)midterm2005_Fall.pdf
Back to MATH150 Login to download
======================================================
Midterm Exam MATH 150: Introduction to Ordinary Di.erential Equations
J. R. Chasnov
2 November 2005
Answer ALL questions Full mark: 60; each question carries 10 marks. Time allowed C 55 minutes
Directions C This is a closed book exam. You may write on the front and back of the exam papers.
Student Name:
Student Number:
Question No. (mark) Marks
1 (10)
2 (10)
3 (10)
4 (10)
5 (10)
6 (10)

Total
Find the solution y = y(x)of thefollowinginitial valueproblem:
x .x
yy =(e . e ),y(0)= .2.
(a)(6pts)With and b given, .nd the solution x = x(t)of thefollowinginitial valueproblem.
be.t(b)(4pts)Determinethe value of t at which x(t)is maximum.
xB+ x =; x(0)=0.
A retiredperson has a sum S(t)investedso astodrawinterest at anannual rate r compounded continuously. Withdrawals for living expenses are made continuously at a rate of k dollars per year. Assume the initial investment S0 and r are .xed.
(a)(6pts)Determinethe withdrawal rate kT such that all the money is spent after exactly T years. (b)(4pts)Determinethe withdrawal rate k at which S(t)will remain constant.
(a)(6pts)Given , .ndthesolutionof thefollowing initial valueproblem: 4x . x =0,x(0)=2,xB(0)= . (b)(4 pts)Determine such that x(t) 0 as t .
(a)(6pts)Given , .ndthesolutionof thefollowing initial valueproblem:
x. 4Bx +5x =0,x(0)=1/2,xB(0)= . (b)(4 pts)Determine such that x(/2) =0.
Find the solution of thefollowinginitial valueproblem:
x+Bx . 2x =2t, x(0)=0,xB(0)=0.