of the following differential equations is homogeneous? wich one (x² + y²) dx + xy dy = 0 + (3 xy²-4y) dx + (x²4 - x) dy = 0 - (+4² - 5x²y) dx + (x³y² + 4xy) dy = 0 x3+y2 (3 xy - 4) dx + (2x² + 3y²) dy = 0
of the following differential equations is homogeneous? wich one (x² + y²) dx + xy dy = 0 + (3 xy²-4y) dx + (x²4 - x) dy = 0 - (+4² - 5x²y) dx + (x³y² + 4xy) dy = 0 x3+y2 (3 xy - 4) dx + (2x² + 3y²) dy = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Of the following differential equations, which one is homogeneous?
![of the following differential equations
is homogeneous?
Wich one
→ (x² + y²) dx + xy dy = 0
(3x4 ²-4y) dx + (x²y - x) dy = (
- (³5²+4²- 5x²y) dx + (x³y ² + 4 xy) dy = 0
(3xy-4) dx + (2x² + 3y²) dy=0
Galaxy A71](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3815c26-984f-482f-ab1c-601d7ee9b88a%2F6d640e98-34d4-479a-9c30-e7a133cdf8c0%2Fi6eio3e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:of the following differential equations
is homogeneous?
Wich one
→ (x² + y²) dx + xy dy = 0
(3x4 ²-4y) dx + (x²y - x) dy = (
- (³5²+4²- 5x²y) dx + (x³y ² + 4 xy) dy = 0
(3xy-4) dx + (2x² + 3y²) dy=0
Galaxy A71
Expert Solution
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Step 1: ''Introduction to the solution''
Recall the fact that a homogenous differential equations are equation that contains homogenous function.
We can solve the homogenous differential equation of the form where
is a homogenous function by simply replacing
.
Important fact: A function of two variables is called homogenous function of degree
if
(1) The given equation is
Now,
is homogenous function of degree 0 and so the given differential equation(1) is homogenous.
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