5. (2xy-y) dx + (x² + x) 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
5-21) Test each of the following equations for exactness and solve the equation. The equations that are not exact may be solved by other methods. Show complete solution.
![ANS. (x + 1) = cx.
5. (2xy- y) dx + (x² + x) dy = 0.
12. (cos x cos y cot x) dx – sin x sin y dy = 0.
13. (r + sin 0- cos 0) dr + r(sin 0 + cos 0) d0 = 0.
ANS. sin x cos y = In c sin xl.
%3D
ANS. r + 2r(sin 0 – cos 0) = c.
14. x(3xy-4y + 6) dx + (x³ – 6x²y? – 1) dy = 0.
ANS. x'y- 2x²y³ + 3x² – y = ċ.
15. (sin 0-2r cos 0) dr + r cos 0(2r sin 0 + 1) d0 = 0.
r sin 0 – r2 cos² 0 = c.
19. |2xy cos (x) = 2xy + 1] dx + [sin (x) – x']dy = 0.
ANS. y[sin (x²) – x²] = c – x.
ANS. x + y? - 3xy = c.
20. (2x- 3y) dx + (2y = 3x) dy
0.
MOMO
21. Do exercise 20 by a second method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9daf6f06-edab-40a1-be68-9cc120cb97b9%2F1fd4dd40-c6cf-4231-81ed-e74e0cb26ec4%2F18wtdbe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ANS. (x + 1) = cx.
5. (2xy- y) dx + (x² + x) dy = 0.
12. (cos x cos y cot x) dx – sin x sin y dy = 0.
13. (r + sin 0- cos 0) dr + r(sin 0 + cos 0) d0 = 0.
ANS. sin x cos y = In c sin xl.
%3D
ANS. r + 2r(sin 0 – cos 0) = c.
14. x(3xy-4y + 6) dx + (x³ – 6x²y? – 1) dy = 0.
ANS. x'y- 2x²y³ + 3x² – y = ċ.
15. (sin 0-2r cos 0) dr + r cos 0(2r sin 0 + 1) d0 = 0.
r sin 0 – r2 cos² 0 = c.
19. |2xy cos (x) = 2xy + 1] dx + [sin (x) – x']dy = 0.
ANS. y[sin (x²) – x²] = c – x.
ANS. x + y? - 3xy = c.
20. (2x- 3y) dx + (2y = 3x) dy
0.
MOMO
21. Do exercise 20 by a second method.
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 4 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
