To determine The general solution of the ordinary differential equation y ′ + y tan x = e − 0.01 x cos x with the initial condition y ( 0 ) = 0 . Explanation The given ordinary differential equation is y ′ + y tan x = e − 0.01 x cos x . The above differential equation is of the form y ′ + p y = r , where p = tan x and r = e − 0.01 x cos x . The general solution is given by, y ( x ) = e − h ( c + ∫ r e h d x ) ... ( 1 ) The integrating factor h is ∫ p d x and it is calculated as follows. ∫ p d x = ∫ tan x d x = ∫ sin x cos x d x = − ∫ d t t ( ∵ cos x = t , − sin x d x = d t ) = − ln ( t ) + c ( ∵ ∫ d x x = ln x ) = − ln ( cos x ) + c Substitute the integrating factor h in equation (1) and obtain the general solution as follows. y ( x ) = e − ( − ln cos x ) ( c + ∫ e − 0.01 x cos x e − ln cos x d x ) = e ln cos x ( c + ∫ e − 0

10th Edition

ISBN: 9781119664697

Author: Kreyszig

Publisher: WILEY

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 1.5, Problem 8P

To determine

The general solution of the ordinary differential equation y′+ytanx=e−0.01xcosx with the initial condition y(0)=0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 1.5, Problem 7P

Chapter 1.5, Problem 9P

Students have asked these similar questions

To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3,700, and the average first-year commission for each new account opened is $5,200. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that individual will open a new account. (a) Determine the equation for computing Gustin's profit per seminar, given values of the relevant parameters. Profit = (3,700 x 5,200) - New Accounts Opened Profit = 5,200 - (New Accounts Opened x 3,700) Profit = (New Accounts Opened x 3,700) - 5,200 Profit = New Accounts Opened - (5,200 × 3,700) Profit = (New Accounts Opened x 5,200) - 3,700 (b) What type of random variable is the number of new accounts opened? Hint: Review Appendix 12.1 for descriptions of various types of probability distributions. continuous integer uniform normal discrete uniform…

Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property, it can then be sold for $158,000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000 and $148,000. (a) What is the estimate of the probability Strassel will be able to obtain the property using a bid of $128,000? (Use at least 5,000 trials. Round your answer three decimal places.) (b) How much does Strassel need to bid to be assured of obtaining the property? $128,000 $138,000 $148,000 (c) Use the simulation model to compute the profit for each trial of…

Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 34,500 miles. Management also believes that the standard deviation is 4,500 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund a portion of the purchase price if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000. Construct a simulation model to answer the following questions. (Use at least 1,000 trials.) (a) For each tire sold, what is the average cost of the promotion (in $)? (Round your answer to two decimal places.) (b) What is the probability that Grear will refund more than $25 for a tire? (Round your answer to three decimal places.)

Chapter 1 Solutions

ADVANCED ENGINEERING MATHEMATICS

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

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.