1. Obtain the General Solution (1-5). 1. (1 — х)у %3D у?. 2. sin x sin y dx + cos x cos y dy = 0. 3. xy dx + e** dy = 0. 4. 2y dx = 3x dy. 5. my dx = nx dy. %3D %3D
1. Obtain the General Solution (1-5). 1. (1 — х)у %3D у?. 2. sin x sin y dx + cos x cos y dy = 0. 3. xy dx + e** dy = 0. 4. 2y dx = 3x dy. 5. my dx = nx dy. %3D %3D
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
100%
![Activity 3: Variable Separable
I.
Obtain the General Solution (1-5).
1. (1 — х)у' %3D у?.
2. sin x sin y dx + cos x cos y dy = 0.
3. ху3 dх + e** dy %3D 0.
4. 2y dx = 3x dy.
5. тy dx — пх dy.
ANS. y In |c(1 – x)| = 1.
ANS. sin y = c cos x.
e-x2
+ y-2 = c.
ANS. x? 3D суз.
ANS. x" 3Dсу".
ANS.
II. Obtain the Particular Solution (6-10).
27. dr/dt = -4rt; when t = 0, r = ro.
28. 2xyy' = 1 + y²; when x = 2, y = 3.
29. хуу 3D 1 + у?; when x %3D2, у %3D 3.
30. 2y dx = 3x dy; when x = 2, y = 1.
r = ro exp (-2t²).
y = /5x – 1.
ANS. y = /10x² – 4.
y = (x/2)²/3.
ANS.
ANS.
ANS.
33. у 3 хехp (у — х?); when x — 0, у %3D 0.
y = In
ANS.
1+ exp(— х?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F200f277e-3742-44cf-9429-5b8f9825a112%2F33f5aa54-03a2-488d-bf2d-f9b93fbd4b72%2Fllipq5c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Activity 3: Variable Separable
I.
Obtain the General Solution (1-5).
1. (1 — х)у' %3D у?.
2. sin x sin y dx + cos x cos y dy = 0.
3. ху3 dх + e** dy %3D 0.
4. 2y dx = 3x dy.
5. тy dx — пх dy.
ANS. y In |c(1 – x)| = 1.
ANS. sin y = c cos x.
e-x2
+ y-2 = c.
ANS. x? 3D суз.
ANS. x" 3Dсу".
ANS.
II. Obtain the Particular Solution (6-10).
27. dr/dt = -4rt; when t = 0, r = ro.
28. 2xyy' = 1 + y²; when x = 2, y = 3.
29. хуу 3D 1 + у?; when x %3D2, у %3D 3.
30. 2y dx = 3x dy; when x = 2, y = 1.
r = ro exp (-2t²).
y = /5x – 1.
ANS. y = /10x² – 4.
y = (x/2)²/3.
ANS.
ANS.
ANS.
33. у 3 хехp (у — х?); when x — 0, у %3D 0.
y = In
ANS.
1+ exp(— х?)
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 7 steps with 6 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)