Exercises: 1. Try solving Example 2 by using method 2. 2. Determine whether the following equation is exact. If it is, then solve it. a. (2x + y)dx + (x- 2y) dy = 0 b. (cos x cos y + 2x) dx – (sin x sin y + 2y) dy = 0 c. cos 0 dr - (r sin 0 – eº) de = 0 3. Given the differential equation (x – 2y) dx + (y – 2x) dy = 0 i. Show that the differential equation is exact. Hence, solve the differential equation by the method of exact equation. ii. Show that the differential equation is homogeneous. Hence, solve the differential equation by the method of homogeneous equation. Check the answer with 3i. 20

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Exercises:
1. Try solving Example 2 by using method 2.
2. Determine whether the following equation is exact. If it is,
then solve it.
a. (2x + y)dx + (x- 2y) dy = 0
b. (cos x cos y + 2x) dx - (sin x sin y + 2y) dy = 0
c. cos 0 dr - (r sin 0 – eº) de = 0
3. Given the differential equation
(x – 2y) dx + (y – 2x) dy = 0
i. Show that the differential equation is exact. Hence, solve
the differential equation by the method of exact equation.
ii. Show that the differential equation is homogeneous.
Hence, solve the differential equation by the method of
homogeneous equation. Check the answer with 3i.
20
Transcribed Image Text:Exercises: 1. Try solving Example 2 by using method 2. 2. Determine whether the following equation is exact. If it is, then solve it. a. (2x + y)dx + (x- 2y) dy = 0 b. (cos x cos y + 2x) dx - (sin x sin y + 2y) dy = 0 c. cos 0 dr - (r sin 0 – eº) de = 0 3. Given the differential equation (x – 2y) dx + (y – 2x) dy = 0 i. Show that the differential equation is exact. Hence, solve the differential equation by the method of exact equation. ii. Show that the differential equation is homogeneous. Hence, solve the differential equation by the method of homogeneous equation. Check the answer with 3i. 20
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