Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
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Question
Chapter 10.6, Problem 4E
To determine
To find:
The formal solution of initial boundary problem.
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Check out a sample textbook solutionStudents have asked these similar questions
65. a. Show that there is no solution to the boundary value problem
у" + 4у —D 0, У(0) — 0, у(п) %3D 1.
b. Show that there are infinitely many solutions to the boundary
value problem
y" + 4y = 0, y(0)
0, у(п) %3D 0.
2) 3
3 dr+du+
+y=t
dr
subject to x = 1 and y = 0 at t = 0
Ex. 5.
Find a solution of Laplace's equation, u +u„ =0, inside a rectangle subject to the following
boundary conditions:
а. и(0, у) 3 0, и(, у) 3 0, и(х,0) — -4sin (2rx). и(х,5) %3 6sin (3rx).
b. и(0), у) - 0, и(, у) - 0, и(х,0) —х', и(x,2) -0.
с. и, (0, у) 3 5sin (ту). и,(1, у)-13sin (2тy), и(х,0) — 0, и(х,2)-0.
d. u, (0, у) — 0, и(1, у) — 0, и(х,0) —0,
и, (х, 2) %35 сos
2
е. и, (0, у) - 0, и, (2л, у) - 0, и(х,-1)-0, и(х,) —1+sin (2xх).
Chapter 10 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - Prob. 6ECh. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...
Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...Ch. 10.2 - In Problems 15-18, solve the heat flow problem...Ch. 10.2 - In Problems 15-18, solve the heat flow problem...Ch. 10.2 - In Problems 15-18, solve the heat flow problem...Ch. 10.2 - In Problems 15-18, solve the heat flow problem...Ch. 10.2 - In Problems 19-22, solve the vibrating string...Ch. 10.2 - In Problems 19-22, solve the vibrating string...Ch. 10.2 - In problem 19-22, solve the vibrating string...Ch. 10.2 - In problem 19-22, solve the vibrating string...Ch. 10.2 - Find the formal solution to the heat flow problem...Ch. 10.2 - Find the formal solution to the vibrating string...Ch. 10.2 - Prob. 25ECh. 10.2 - Verify that un(x,t) given in equation 10 satisfies...Ch. 10.2 - Prob. 27ECh. 10.2 - In Problems 27-30, a partial differential equation...Ch. 10.2 - Prob. 29ECh. 10.2 - In Problems 27-30, a partial differential equation...Ch. 10.2 - For the PDE in Problem 27, assume that the...Ch. 10.2 - For the PDE in Problem 29, assume the following...Ch. 10.2 - Prob. 33ECh. 10.3 - In Problems 1 -6, determine whether the given...Ch. 10.3 - In Problems 1 -6, determine whether the given...Ch. 10.3 - In Problems 1 -6, determine whether the given...Ch. 10.3 - In Problems 1 -6, determine whether the given...Ch. 10.3 - In Problems 1 -6, determine whether the given...Ch. 10.3 - In Problems 1 -6, determine whether the given...Ch. 10.3 - 7. Prove the following properties: a. If f and g...Ch. 10.3 - Verify the formula 5. Hint: Use the identity...Ch. 10.3 - In Problems 9-16, compute the Fourier series for...Ch. 10.3 - In Problems 9-16, compute the Fourier series for...Ch. 10.3 - In Problems 9-16, compute the Fourier series for...Ch. 10.3 - In Problems 9-16, compute the Fourier series for...Ch. 10.3 - In Problems 9-16, compute the Fourier series for...Ch. 10.3 - In Problems 17 -24, determine the function to...Ch. 10.3 - In Problems 17 -24, determine the function to...Ch. 10.3 - In Problems 17 -24, determine the function to...Ch. 10.3 - In Problems 17 -24, determine the function to...Ch. 10.3 - In Problems 17 -24, determine the function to...Ch. 10.3 - In Problems 17 -24, determine the function to...Ch. 10.3 - In Problems 17 -24, determine the function to...Ch. 10.3 - In Problems 17 -24, determine the function to...Ch. 10.3 - 25. Find the functions represented by the series...Ch. 10.3 - Show that the set of functions...Ch. 10.3 - Find the orthogonal expansion generalized Fourier...Ch. 10.3 - a. Show that the function f(x)=x2 has the Fourier...Ch. 10.3 - In Section 8.8, it was shown that the Legendre...Ch. 10.3 - As in Problem 29, find the first three...Ch. 10.3 - The Hermite polynomial Hn(x) are orthogonal on the...Ch. 10.3 - The Chebyshev Tchebichef polynomials Tn(x) are...Ch. 10.3 - Let {fn(x)} be an orthogonal set of functions on...Ch. 10.3 - Norm. The norm of a function f is like the length...Ch. 10.3 - Prob. 35ECh. 10.3 - Complex Form of the Fourier Series. a. Using the...Ch. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.4 - In Problems 1-4, determine a the -periodic...Ch. 10.4 - In Problem 1-4, determine a the -periodic...Ch. 10.4 - In Problems 1-4, determine a the -periodic...Ch. 10.4 - In Problem 1-4, determine a the -periodic...Ch. 10.4 - In Problems 5 -10, compute the Fourier sine series...Ch. 10.4 - In Problems 5 -10, compute the Fourier sine series...Ch. 10.4 - In Problems 5 -10, compute the Fourier sine series...Ch. 10.4 - In Problems 5 -10, compute the Fourier sine series...Ch. 10.4 - In Problems 5 -10, compute the Fourier sine series...Ch. 10.4 - In Problems 5 -10, compute the Fourier sine series...Ch. 10.4 - In Problems 11 -16, compute the Fourier cosine...Ch. 10.4 - In Problems 11 -16, compute the Fourier cosine...Ch. 10.4 - In Problems 11 -16, compute the Fourier cosine...Ch. 10.4 - In Problems 11 -16, compute the Fourier cosine...Ch. 10.4 - In Problems 11 -16, compute the Fourier cosine...Ch. 10.4 - In Problems 11 -16, compute the Fourier cosine...Ch. 10.4 - In Problems 17 -19, for the given f(x), find the...Ch. 10.4 - In Problems 17 -19, for the given f(x), find the...Ch. 10.4 - In Problems 17 -19, for the given f(x), find the...Ch. 10.5 - In Problems 1 -10, find a formal solution to the...Ch. 10.5 - In Problems 1 -10, find a formal solution to the...Ch. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - In Problems 1 -10, find a formal solution to the...Ch. 10.5 - In Problems 1 -10, find a formal solution to the...Ch. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - In Problems 1-10, find a formal solution to the...Ch. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Find a formal solution to the initial boundary...Ch. 10.5 - Prob. 14ECh. 10.5 - In Problems 15-18, find a formal solution to the...Ch. 10.5 - In Problems 15-18, find a formal solution to the...Ch. 10.5 - In Problems 15-18, find a formal solution to the...Ch. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.6 - In Problems 1 -4, find a formal solution to the...Ch. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - The Plucked String. A vibrating string is governed...Ch. 10.6 - Prob. 6ECh. 10.6 - Prob. 7ECh. 10.6 - In Problems 7 and 8, find a formal solution to the...Ch. 10.6 - If one end of a string is held fixed while the...Ch. 10.6 - Derive a formula for the solution to the following...Ch. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - In Problems 13 -18, find the solution to the...Ch. 10.6 - In Problems 13 -18, find the solution to the...Ch. 10.6 - In Problems 13 -18, find the solution to the...Ch. 10.6 - In Problems 13 -18, find the solution to the...Ch. 10.6 - Derive the formal solution given in equation 22-24...Ch. 10.7 - In Problems 1-5, find a formal solution to the...Ch. 10.7 - Prob. 3ECh. 10.7 - In Problems 1-5, find a formal solution to the...Ch. 10.7 - Prob. 6ECh. 10.7 - In Problem 7 and8, find a solution to the...Ch. 10.7 - In Problems 7 and 8, find a solution to the...Ch. 10.7 - Find a solution to the Neumann boundary value...Ch. 10.7 - Prob. 13ECh. 10.7 - Prob. 15ECh. 10.7 - Prob. 16ECh. 10.7 - Prob. 18ECh. 10.7 - Prob. 19ECh. 10.7 - Stability.Use the maximum principle to prove the...Ch. 10.7 - Prob. 21E
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