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...
Related questions
Question
Homogeneous DE
M(x,y)dx + N(x,y)dy = 0
is Homogeneous if both M and N are homogeneous functions of the same order.
A function f(x,y) is called homogeneous of degree n if
f(ʎx, ʎy) = ʎnf(x,y)
Solution Steps:
Objective: To reduce into a Variable Separable Form
a. Replace y by ux or x by vy
if y = ux, dy = udx + xdu . Use y=ux if N is simpler in form.
if x = vy, dx = vdy + ydv . Use x=y if M is simpler in form
b. Simplify the resulting equation
c. Separate the variables
d. Integrate both sides of the equation to get the General Solution
e. Substitute u = y/x or v = x/y to have the GS in terms of x and y
have C which is arbitrary constant
Solve the DE. (Homogeneous DE)
1. (x-2y)dx + (2x+y)dy = 0
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