(a) Verify that the one-parameter family y 2 2y = x 2 x + c...
Question:
(a) Verify that the one-parameter family y2 2y = x2 x + c is an implicit solution of the differential equation (2y 2)y' = 2x 1.
(b) Find a member of the one-parameter family in part (a) that satisfies the initial condition y(0) = 1.
(c) Use your result in part (b) to find an explicit function y = ϕ(x) that satisfies y(0) = 1. Give the domain of the function ϕ. Is y = ϕ(x) a solution of the initial-value problem? If so, give its interval I of definition; if not, explain
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (9 reviews)
a Differentiating y 2 2y x 2 x c we obtain 2yy 2y 2x1 or 2y 2y 2x1 b Setting x 0 and y 1 in the so...View the full answer
Answered By
Rustia Melrod
I am a retired teacher with 6 years of experience teaching various science subjects to high school students and undergraduate students. This background enables me to be able to help tutor students who are struggling with the science of business component of their education. Teaching difficult subjects has definitely taught me patience. There is no greater joy for me than to patiently guide a student to the correct answer. When a student has that "aha!" moment, all my efforts are worth it.
The Common Core standards are a useful yardstick for measuring how well students are doing. My students consistently met or exceeded the Common Core standards for science. I believe in working with each student's individual learning styles to help them understand the material. If students were struggling with a concept, I would figure out a different way to teach or apply that concept. I was voted Teacher of the Year six times in my career. I also won an award for Innovative Teaching Style at the 2011 National Teaching Conference.
4.90+
4+ Reviews
10+ Question Solved
Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
Question Posted:
Students also viewed these Mathematics questions
-
A Washington Post/ Kaiser Family Foundation poll taken July 25 to August 5, 2012, asked a random sample of 3130 adults: Do you support or oppose putting a special tax on junk foodthat is, things like...
-
For each of the non-homogeneous linear DEs in Problems (a) Verify that the given y1, y2, y3 satisfy the corresponding homogeneous equation. (b) Use the Superposition Principle, with appropriate...
-
In Problem 21 a one-parameter family of solutions of the DE P' = P(1 P) is given. Does any solution curve pass through the point (0, 3)? Through the point (0, 1)? Data from problem 21 Verify that the...
-
The IASB's main objective is to develop a set of high-quality standards for financial reporting by companies at the international level. Required: Critically examine the possibility of achieving this...
-
Biz Zing Inc. (BZI) provides life and work counselling to companies. At the end of 2013, BZI's total assets were $1,120. BZI's unadjusted trial balance includes the following for the twelve months...
-
Business 2.0 recently reported on Mens Warehouses CEO George Zimmers policy that no employee or interviewee will ever undergo a criminal background check. The company, however, loses an average of...
-
Assume that $y_{i j}$ are i.i.d and follow a normal distribution with variance $\sigma^{2}$. Under the null hypothesis that a factorial effect 0 , a. Show that \[\frac{\bar{y}_{+}-\bar{y}_{-}}{s / 2}...
-
Presented below are a number of facts related to Weller, Inc. Assume that no mention of these facts was made in the financial statements and the related notes. Instructions Assume that you are the...
-
Lev and Gu are surprised that the structure and content of corporate annual reports have not changed between 1 9 0 2 and 2 0 1 2 . Why would one expect the accounting system to change over time? 2 -...
-
Matusek Corporation has been experiencing a higher than expected number of warranty claims in the current year, due mainly to less than ideal product design. For this reason, the warranty expense...
-
What skills are necessary in a good marketer?
-
(a) Give the domain of the function y = x 2/3 . (b) Give the largest interval I of definition over which y = x 2/3 is solution of the differential equation 3xy' 2y = 0.
-
(a) Where does the normal line to the ellipse x2 xy + y2 = 3 at the point ( 1, 1) intersect the ellipse a second time? (See page 192 for the definition of a normal line.) (b) Illustrate part (a) by...
-
Alaska Airlines employed Tellis in Seattle as a maintenance mechanic. His wife was having difficulties with her pregnancy, so on the morning of July 4, 2000, he told his supervisor he needed to take...
-
Explain what happened with the joint tenancy with right of survivorship. Who owns what now? Does Countrywide have a mortgage? Are Troy and Judy liable for the mortgage? Is their property subject to...
-
The Cost of Goods Sold (COGS) for a manufacturing unit in 2020 was $150 million. The manufacturing units beginning and ending inventories were $20 million and $4 million respectively. What is the...
-
The following information pertains to the defined benefit pension plan of Curtis Orchard Company for the year: Service cost $ 80,000 Cash contributions 160,000 Benefits paid to retirees 110,000 Plan...
-
Gabrielle Student makes $60,000 her first year out of Creighton University. She is still single. Her paychecks have had $6200 in federal income taxes withdrawn. 2. Garbrielle has $15,000 of itemized...
-
Which of the strategies discussed in this chapter are these companies using? Explain.
-
Repeat the previous problem, but close the positions on September 20. Use the spreadsheet to find the profits for the possible stock prices on September 20. Generate a graph and use it to identify...
-
If we assume that {f(t)/t} exists and {f(t)} = F(s), then Use this result to find the Laplace transform of the given function. The symbols a and k are positive constants. (a) f(t) = sin at/t (b) f(t)...
-
Because f(t) = ln t has an infinite discontinuity at t = 0 it might be assumed that {ln t} does not exist; however, this is incorrect. The point of this problem to guide you through the formal steps...
-
In this problem you are led through the commands in Mathematica that enable you to obtain the symbolic Laplace transform of a differential equation and the solution of the initial-value problem by...
-
How does culture relate to political and security issues in the world? Please provide specific examples. 2 What are the most significant contemporary security issues in the world? How does culture...
-
Tree Seedlings has the following current-year purchases and sales for its only product. Units Acquired at Cost Date January 1 Activities Beginning inventory January 3 Sales February 14 February 15...
-
A cylindrical log is cut as shown to form a park bench. Find: a. The area of triangle OAB in m. [2] b. The volume of the log in m. [3] B 70% 40 cm 3m
Study smarter with the SolutionInn App