Question: (a) Coefficient formulas, show how a and b in (1) can be expressed in terms of 1 and 2. Explain how these formulas can be

(a) Coefficient formulas, show how a and b in (1) can be expressed in terms of λ1 and λ2. Explain how these formulas can be used in constructing equations for given bases.
(b) Root zero, solve y" + 4y" = 0 (i) by the present method, and (ii) by reduction to first order. Can you explain why the result must be the same in both cases? Can you do the same for a general ODE y" + ay' = 0?
(c) Double root, verify directly that xeλx with λ = – a/2 is a solution of (1) in the case of a double root. Verify and explain why y = e–2x is solution of y" – y' – 6y = 0 but xe–2x is root.
(d) Limits double roots should be limiting cases of distinct roots λ1, λ1 as, say, λ2 → λ1. Experiment with this idea. (Remember 1’Hopital’s rule from calculus.) Can you arrive at xeλ1x? Give it a try.

Step by Step Solution

★★★★★

3.40 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Team Project A We obtain A A dd a b 0 Comparison of coefficients ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

M-C-D-E (192).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

The data from Problem P9.20 can be expressed in terms of the molality rather than the mole fraction of Br2 . Use the data from the following table and a graphical method to determine the Henrys law...

Show that T1/T0 can be expressed in terms of m2/m1 ≡ a and cos ψ ≡ y as Plot T1/T0 as a function of ψ for a = 1, 2, 4, and 12. These plots correspond to the energies of protons or...

Any analysis of variance model can be expressed in terms of the general linear model y = x + , where the X matrix consists of 0s and 1s. Show that the single-factor model y ij = + i , ij , i = 1,...

Section 2.2: p. 2, 4, 12, 24, 30. Please solve these problems according to the method mentioned in their respective headings. 1-14 GENERAL SOLUTION 27. 10y" + 5y' + 0.625y = 0, y(0) = 2, y'(0) = -4.5...

Question 1 Continue with the setting o f Homework 3 . But now add the assumption that the aggregate endowment o f the three consumption goods i s some vector ( y 1 , y 2 , y 3 ) i n R + + 3 that...

Please answer E, F, G only. Digital Controls, Inc. (DCI) manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per...

Digital Controls, Inc. (DCI) manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller...

Question 1 Financial statements are prepared for a range of different business entities. 1. Identify the different entities financial statements can be prepared for. 2. Identify the different...

please give a summary of this article I really need it for a class!!!!!! thank you so much!!! ASSET ALLOCATION: MANAGEMENT STYLE AND PERFORMANCE MEASUREMENT An Asset class factor model can help make...

Discuss and explain the method of impulse testing of high Voltages Transformer (or) Power Transformer

For each of the following differential equations modeling an LTIC system, determine (a) the zero- input response, (b) the zero-state response, (c) the overall response and (d) the steady state...

10 Write the correct sign, , between each pair of numbers. a -2.3-2.4 C -0.15 -0.08 b -7.23 -7.23 -7.29 d -11.02 -11.5

Because of the outbreak of Covid-19, the S&P 500 stock index fell over 30% from its recent high level. At the same time, the volatility index of the S&P 500 (a measure of the market's...

On April 1, 2020, Summit County issued $10,000,000 in variable rate debt, with interest paid on March 31 of each year, the county's fiscal year-end. The variable rate is adjusted at the beginning of...

Use the following information for Taco Swell, Incorporated, (assume the tax rate is 21 percent): Sales Depreciation Cost of goods sold Other expenses Interest Cash Accounts receivable Short-term...

Revised Car Purchase Agreement Revise your draft of the Car Purchase Agreement based on the material that you have covered so far this semester. In addition, include appropriate provisions to reflect...

Barry Allen forms a new corporation with him as the sole shareholder. He transfers equipment that he bought for $200,000. The note still owing on the equipment is $75,000. He utilized Section 179 and...

You need to borrow $1000 for an emergency. You have two alternatives. One is to borrow from a bank. The other is to borrow from your childhood friend Greta Ganav, who is in the private financing...

Chace Products is a division of a major corporation. Last year the division had total sales of $21, 300,000, net operating income of $675100, and average operating assets of $5.000,000. The company's...

Please show the work. thank you Suppose we have the following Treasury bill returns and inflation rates over an eight year period: Year Treasury Bills Inflation 1 7.55% 9.02% 2 8.29 12.69 3 6.15 7.24...

Find the EAR in each of the following cases. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. Use 365 days in a year.)