To determine To solve: The ODE x 2 y ″ − 5 x y ′ + 9 y = 0 by reducing to first order ODE where y 1 = x 3 . Explanation The given ODE is x 2 y ″ − 5 x y ′ + 9 y = 0 which can be rewritten as y ″ − 5 x y ′ + 9 x 2 y = 0 . Also, one of the solution is y 1 = x 3 . Compare the given ODE with y ″ + p y ′ + q y = r . Here, p = − 5 x , q = 9 x 2 , and r = 0 . That implies, e − ∫ p d x = e − ∫ − 5 x d x = e 5 ln | x | = e ln | x | 5 = x 5 Compute the second solution as follows. The general form to compute the second solution is y 2 = y 1 u = y 1 ∫ U d x . It is known that, U = 1 y 1 2 e − ∫ p d x . Substitute e − ∫ p d x = x 5 in U = 1 y 1 2 e − ∫ p d x and simplify further

10th Edition

ISBN: 9781119480150

Author: Kreyszig

Publisher: WILEY C

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 2.1, Problem 9P

To determine

To solve: The ODE x2y″−5xy′+9y=0 by reducing to first order ODE where y1=x3.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.1, Problem 8P

Chapter 2.1, Problem 10P

Students have asked these similar questions

4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.

3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.

2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…

Chapter 2 Solutions

ADVANCED ENGINEERING MATH.>CUSTOM<

Knowledge Booster

$Advanced Math$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.