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Math 1

This document provides a test for an Ordinary Differential Equations course. The test contains 6 questions worth a total of 40 marks. Question 1 asks students to find a particular solution for a given initial value problem. Question 2 asks students to solve a first order differential equation. Question 3 asks students to solve another first order differential equation with an initial condition. Question 4 asks students to find constants in an exact differential equation. Questions 5 and 6 ask students to solve differential equations by finding appropriate integrating factors.

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Cha Lee
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45 views1 page

Math 1

This document provides a test for an Ordinary Differential Equations course. The test contains 6 questions worth a total of 40 marks. Question 1 asks students to find a particular solution for a given initial value problem. Question 2 asks students to solve a first order differential equation. Question 3 asks students to solve another first order differential equation with an initial condition. Question 4 asks students to find constants in an exact differential equation. Questions 5 and 6 ask students to solve differential equations by finding appropriate integrating factors.

Uploaded by

Cha Lee
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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ORDINARY DIFFERENTIAL EQUATIONS January 2014

TEST 1
(10 % coursework)

Instructions: Answer ALL questions. Time allocation: 1H30.

1. Find a particular solution for the following initial-value problem that satisfy the prescribed initial
conditions
d2y
x 2 2  x  10 y  0 ; y1  2 , y1  5
dy
dx dx

if the general solution to the differential equation is yx  c1x cos3ln x   c2 x sin3ln x .
[5 marks]

2. Solve the following first order differential equation

xydx  3e x dy  0 .
[5 marks]

3. Solve the following first order differential equation

x  3 dz  z  2 ln x ; z1  15 .
dx
[5 marks]

4. Find the values of the constants a, b and c (if any) if the differential equation given is Exact.

dy
2 x a y b  4 x3  cx 2 y 3 0
dx
[5 marks]

5. Solve (2 y 2  2 y  4 x 2 )dx  (2 xy  x)dy  0 by finding an appropriate integrating factor


[10 marks]

6. Solve xy  2 y  xy 3
[10 marks]

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