Explanation Approach: Consider, J 1 2 ( t ) = 2 π t ( sin t ) = J ... ( 1 ) Y 1 2 ( t ) = − 2 π t ( cos t ) = Y ... ( 2 ) Calculation: Consider the given function, y ″ + 1 t y ′ + ( 1 − n 2 t 2 ) y = 0 Differentiate equation ( 1 ) with respect to t . J ′ = d d t ( 2 π t ( sin t ) ) = 2 π ( 2 t cos t − sin t 2 t t ) ... ( 3 ) Differentiate equation ( 3 ) with respect to t . J ″ = d d t ( 2 π t ( 2 t cos t − sin t 2 t t ) ) = 2 π t ( 2 t t cos t − 4 t 2 t sin t − 6 t t cos t + 3 t sin t 4 t 3 2 t 3 2 ) = 2 π ( 2 t cos t − 4 t 2 sin t − 6 t cos t + 3 sin t 4 t ( t 3 2 ) ) Now, for n = 1 2 Substitute 2 π t ( sin t ) for y , ( 2 π ( 2 t cos t − sin t 2 t t ) ) for y ′ , and 2 π ( 2 t cos t − 4 t 2 sin t − 6 t cos t + 3 sin t 4 t ( t 3 2 ) ) for y ″ in the given function. = 2 π ( 2 t cos t − 4 t 2 sin t − 6 t cos t + 3 sin t 4 t ( t 3 2 ) ) + 1 t ( 2 π ( 2 t cos t − sin t 2 t t ) ) + ( 1 − n 2 t 2 ) ( 2 π t ( sin t ) ) = 2 π ( sin t ( 1 − 4 t 2 ) 4 t 2 t + ( 1 − n 2 t 2 ) sin t t ) = 0 Similarly, Differentiate equation ( 2 ) with respect to t

7th Edition

ISBN: 9780321977175

Author: Nagle

Publisher: PEARSON CO

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 4.8, Problem 14E

To determine

To verify:

The formulas for the Bessel functions J1/2(t), Y1/2(t) do indeed solve the given equation.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.8, Problem 13E

Chapter 4.8, Problem 15E

Students have asked these similar questions

Consider the following hypothesis test. The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n 1 = 80 n 2 = 70 x 1 = 104 x 2 = 106 σ 1 = 8.4 σ 2 = 7.6 What is the value of the test statistic? If required enter negative values as negative numbers (to 2 decimals). What is the p-value (to 4 decimals)? Use z-table. With = .05, what is your hypothesis testing conclusion?

Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use = .05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A Consultant B = 16 = 10 = 6.82 = 6.25 = .64 = .75 State the null and alternative hypotheses.H0: 1 - 2 Ha: 1 - 2 Compute the value of the test statistic (to 2 decimals). What is the p-value?The p-value is What is your conclusion?

A firm paid its first annual dividend yesterday in the amount of $.15 per share. The company plans to double the dividend in each of the next 3 years. Starting in Year 4, the firm plans to pay $1.50 per share indefinitely. What is one share of this stock worth today if the market rate of return on similar securities is 13.8 percent? Multiple Choice $11.79 $8.92 $10.77 $11.02 $10.26

Chapter 4 Solutions

EBK FUND.OF DIFF.EQUATIONS+BOUNDARY...

Ch. 4.1 - Verify that for b=0 and Fext(t)=0, equation (3)...Ch. 4.1 - If Fext(t)=0, equation (3) becomes my+by+ky=0. For...Ch. 4.1 - Show that if Fext(t)=0, m=1, k=9, and b=6, then...Ch. 4.1 - Prob. 4E Ch. 4.1 - Verify that the exponentially damped sinusoid...Ch. 4.1 - An external force F(t)=2cos2t is applied to a...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - Undamped oscillators that are driven at resonance...

Knowledge Booster

Learn more about

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

To verify: The formulas for the Bessel functions J 1 / 2 ( t ) , Y 1 / 2 ( t ) do indeed solve the given equation.

Solution Summary: The author explains that the formulas for the Bessel functions J_1/2(t),

Concept explainers

Videos

To verify:

The formulas for the Bessel functions J1/2(t), Y1/2(t) do indeed solve the given equation.

Want to see the full answer?

Chapter 4 Solutions

To verify: The formulas for the Bessel functions J 1 / 2 ( t ) , Y 1 / 2 ( t ) do indeed solve the given equation.

Solution Summary: The author explains that the formulas for the Bessel functions J_1/2(t),

Concept explainers

Videos

To verify: The formulas for the Bessel functions J1/2(t), Y1/2(t) do indeed solve the given equation.

Want to see the full answer?

Chapter 4 Solutions

To verify:

The formulas for the Bessel functions J1/2(t), Y1/2(t) do indeed solve the given equation.