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Semester II 2009/2010

The University of the West Indies Course Code 20././ DO NOT WRITE OR TYPE ON THE BACK OF THIS SHEET: USE ONE SIDE ONLY INSTRUCTIONS: Each page must be signed by the First and Second Examiners, and where applicable the University and External Examiners. Completed forms should be handed to the Senior/Assistant Registrar (Examinations). Where applicable, the EXTERNAL EXAMINER is required to sign the question paper and return it with comments, if any, (on a separate sheet), to the Senior/Assistant Registrar (Examinations).

...........First Examiner University Examiner (where applicable)

. ..Second Examiner External Examiner (where applicable)

Date: 20../../ Date: 20../../

SEMESTER II 2009/2010

The University of the West Indies Course Code 20././ DO NOT WRITE OR TYPE ON THE BACK OF THIS SHEET: USE ONE SIDE ONLY INSTRUCTIONS: Each page must be signed by the First and Second Examiners, and where applicable the University and External Examiners. Completed forms should be handed to the Senior/Assistant Registrar (Examinations). Where applicable, the EXTERNAL EXAMINER is required to sign the question paper and return it with comments, if any, (on a separate sheet), to the Senior/Assistant Registrar (Examinations).

...........First Examiner University Examiner (where applicable)

. ..Second Examiner External Examiner (where applicable)

Date: 20../../ Date: 20../../

THE UNIVERSITY OF THE WEST INDIESSemester l Semester II Supplemental/Summer School Examinations of December /April/May /July 2010Originating Campus: Cave Hill Mona St. Augustine Mode: On Campus By Distance Course Code and Title: M32Q Solutions of differential equations

Date:May 6, 2010Time: 1.00pm-3.00pm

Duration:2Hours.Paper No: 1

Materials required: Answer booklet: Normal Special Not required Calculator: Programmable Non Programmable (where applicable) Multiple Choice answer sheets: numerical alphabetical 1-20 1-100

Auxiliary/Other material(s) Please specify:

Candidates are permitted to bring the following items to their desks: Non Programmable Calculator

Instructions to Candidates: This paper has 3 pages (including this one) & 4 questions. The weight of the paper is 60%.You must answer ALL questions.The use of calculators is not permitted.Marks will be lost for an approximate answer where a precise answer is possible.

Candidates are reminded that the examiners shall take into account the proper use of the English Language in determining the mark for each response.

Question 1 (10 points)

Find the explicit solution of the following initial value problem

, [3 points]

Find the general solutions of the following ordinary differential equations

for ; [2 points]

; [2 points]

; [3 points]

Do not leave complex numbers in your answers.

Problem 2 (10 points)

The motion of a simple rigid pendulum without friction can be described by the differential equation

where and is the angle the pendulum makes with the downward vertical.

Let . Show that [3 points]

It follows from (a) that the pendulum equation can be written as [7 points]

Solve this equation.

You may leave the solution in the implicit form.

Problem 3 (20 points)

Let. Solve the following initial value problem

,

with [20 points]

by means of the Laplace transform method.

Problem 4 (20 points)

Consider the third order homogeneous differential equation with constant coefficients

(1)

(5 points) Transform the above equation into a system of first order differential equations of the form

. [5 points]

where A is a 3x3 matrix.

What is the general solution of the system derived in (a)? [10 points]

What is the general solution of equation (1)? [5 points]

END OF PAPER

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