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. xdx + sin2 (y/x) [ydx - xdy = 0]
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. xdx + sin2 (y/x) [ydx - xdy = 0]
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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. xdx + sin2 (y/x) [ydx - xdy = 0]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 5 images
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning