If the right side of the equationx, y) can be expressed as a function of the ratio only, then the equation is said to be homogeneous. Such equations can always be transformed into separable equations by a change of the dependent variable. The following method outline can be used for any homogeneous equation. That is, the substitution y=xv(x) transforms a homogeneous equation into a separable equation. The latter equation can be solved by direct integration, and then replacing v by gives the solution to the original equation. (x² + 3xy + y²) x - x² dy = 0 (a) Show that the given equation is homogeneous. Dividing by x², we see that the equation becomes (1+ (b) Solve the differential equation. dx-dy. Hence the differential equation Select homogeneous.
If the right side of the equationx, y) can be expressed as a function of the ratio only, then the equation is said to be homogeneous. Such equations can always be transformed into separable equations by a change of the dependent variable. The following method outline can be used for any homogeneous equation. That is, the substitution y=xv(x) transforms a homogeneous equation into a separable equation. The latter equation can be solved by direct integration, and then replacing v by gives the solution to the original equation. (x² + 3xy + y²) x - x² dy = 0 (a) Show that the given equation is homogeneous. Dividing by x², we see that the equation becomes (1+ (b) Solve the differential equation. dx-dy. Hence the differential equation Select homogeneous.
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
answer pls.
![If the right side of the equation = f(x, y) can be expressed as a function of the ratio only, then the equation is said to be homogeneous. Such equations can always be transformed into separable equations by a change of the dependent variable.
The following method outline can be used for any homogeneous equation. That is, the substitution y = xv(x) transforms a homogeneous equation into a separable equation. The latter equation can be solved by direct integration, and then replacing v by gives the solution to the original equation.
(x² + 3xy + y²) dx - x² dy = 0
(a) Show that the given equation is homogeneous.
Dividing by x², we see that the equation becomes (1+
(b) Solve the differential equation.
(c) Draw a direction field and some integral curves.
Are they symmetric with respect to the origin?
O Yes
O No
Jdx dy. Hence the differential equation
-Select- homogeneous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb52044d-d588-4d60-8413-960f544d05a0%2Fc3d5b97e-3946-4687-89e8-b42fb7070e46%2F2d6xz9s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If the right side of the equation = f(x, y) can be expressed as a function of the ratio only, then the equation is said to be homogeneous. Such equations can always be transformed into separable equations by a change of the dependent variable.
The following method outline can be used for any homogeneous equation. That is, the substitution y = xv(x) transforms a homogeneous equation into a separable equation. The latter equation can be solved by direct integration, and then replacing v by gives the solution to the original equation.
(x² + 3xy + y²) dx - x² dy = 0
(a) Show that the given equation is homogeneous.
Dividing by x², we see that the equation becomes (1+
(b) Solve the differential equation.
(c) Draw a direction field and some integral curves.
Are they symmetric with respect to the origin?
O Yes
O No
Jdx dy. Hence the differential equation
-Select- homogeneous.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)