Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. (y - x)y' = y - x + 2; y = x + 2√x + 3 When y = x + 2√x + 3, y' = Thus, in terms of x, (y - x)y' = y-x + 2 = Since the left and right hand sides of the differential equation are equal when x + 2√x + 3 is substituted for y, y = x + 2√x + 3 is a solution. Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.) Then by considering as a solution of the differential equation, give at least one interval I of definition. O (-6, 3) O (-6, -3] O (-∞, -3) O (-3,00) [-3, 3] Need Help? Watch It Read It
Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. (y - x)y' = y - x + 2; y = x + 2√x + 3 When y = x + 2√x + 3, y' = Thus, in terms of x, (y - x)y' = y-x + 2 = Since the left and right hand sides of the differential equation are equal when x + 2√x + 3 is substituted for y, y = x + 2√x + 3 is a solution. Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.) Then by considering as a solution of the differential equation, give at least one interval I of definition. O (-6, 3) O (-6, -3] O (-∞, -3) O (-3,00) [-3, 3] Need Help? Watch It Read It
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
![Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation.
(y - x)y' = y - x + 2; y = x + 2√x + 3
When y = x + 2√x + 3,
y' =
Thus, in terms of x,
(y - x)y' =
y-x + 2 =
Since the left and right hand sides of the differential equation are equal when x + 2√x + 3 is substituted for y, y = x + 2√x + 3 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.)
Then by considering as a solution of the differential equation, give at least one interval I of definition.
O (-6, 3)
O (-6, -3]
O (-∞, -3)
O (-3,00)
[-3, 3]
Need Help?
Watch It
Read It](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc1a3404-9522-46f8-b9d5-d94c2e091e17%2F3f7b6c79-cbf2-4c03-9cd6-878e8b9a4acd%2Fq3uekc_processed.png&w=3840&q=75)
Transcribed Image Text:Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation.
(y - x)y' = y - x + 2; y = x + 2√x + 3
When y = x + 2√x + 3,
y' =
Thus, in terms of x,
(y - x)y' =
y-x + 2 =
Since the left and right hand sides of the differential equation are equal when x + 2√x + 3 is substituted for y, y = x + 2√x + 3 is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.)
Then by considering as a solution of the differential equation, give at least one interval I of definition.
O (-6, 3)
O (-6, -3]
O (-∞, -3)
O (-3,00)
[-3, 3]
Need Help?
Watch It
Read It
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 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,
