Consider the following initial-value problem. Consider the following initial-value problem.y" - 6y = 0, y(0) = 1, y'(0) = 9Solve the given problem first using the form of the general solution given in (10) in Section 4.3.-kxy = c₁ekx + c₂e-(10)

Consider the following initial-value problem..Solve the given problem first using the form of the…

Answered: Consider the following initial-value…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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#1) You are transporting ice cream from a warehouse to a local shop in a refrigerated van. Before you get on the road, the cargo area of the van is cooled to 15 °F. After 30 minutes of driving, you stop for gas and check the cargo area again. Disaster! The door isn't closing properly, and the cargo area of the van has warmed to 24 °F. It's a cool morning, at a constant 50 °F outside. If the cargo area of the van warms to 32 °F, then the ice cream will start to melt. But your destination is 30 more minutes away. Can you deliver the ice cream to the shop before it starts to melt?
In Problems 27-36, solve the given initial-value problem.
Which of the following is the solution of the following initial value problem y' + y = 0; y(3) = 2 ? а. у (х) — 2е*-з b. У(х) — 2е**з с. у (х) — 2е-х+3 d. y(x) = e* e. у (х) %3 Зе**2
8. Solve the following initial value problem: (picture)
(4).
In each of Problems 1 through 8, determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.
4. Solve the following initial value problem: S2y = y +e; ly(0) = -1.
Question 16 Suppose that you have downloaded data on the daily share prices for a company for the period from the start of 2020 to the end of 2020 from the website of Yahoo Finance UK. You have also calculated the daily rates of return for the company's shares as (closing price - opening price)/opening price. By using the knowledge that you have gained from descriptive statistics, how can you obtain useful information about the company's share performance in terms of risk and return using a range of alternative indicators? Note that you should give necessary formulas for the technical concepts wherever they may apply.
4. Solve the following initial value problem dy 2y y(1) = 3. dr
Justify and analyze the model proposed in equation (2), covering in particular the following issues: an analysis of the validity of equation (2) as a model for the fish population in a fish farm; an analysis of whether, based on model equation (2), we may expect a stable fish population from which harvesting could take place; and, if so, an analysis of how large an initial population of fish will be required to obtain this stable population and the length of time required for the stable population to be established (numerical solver recommended).

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Consider the following initial-value problem. y" - 6y = 0, y(0) = 1, y'(0) = 9 Solve the given problem first using the form of the general solution given in (10) in Section 4.3. + c₂e-Kx (10) y = c₁ekx