3rd Edition

ISBN: 9780134696454

Author: Sauer, Tim

Publisher: Pearson,

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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…

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Textbook Question

Chapter 7.1, Problem 3E

Consider the BVP { y ′ ′ = c y y ( a ) = y a y ( b ) = y b where c > 0 , a < b

Show that there exists a unique solution

y ( t ) on [ a , b ] .

Find a solution of form

y ( t ) = c 1 e d 1 t + c 2 e d 2 t for some c 1 , c 2 , d 1 , d 2 .

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Chapter 7.1, Problem 2E

Chapter 7.1, Problem 4E

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Chapter 7 Solutions

Numerical Analysis

Ch. 7.1 - Use Theorem 7.1 to prove that the boundary value...Ch. 7.1 - Show that the solutions to the BVPs in Exercise 1...Ch. 7.1 - Consider the BVP { y=cyy(a)=yay(b)=yb where c0, ab...Ch. 7.1 - Consider the BVP { y=cyy(0)=0y(b)=0 where c0. For...Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Show that the solutions to the linear BVPs {...Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Apply the Shooting Method to the linear BVPs....

Ch. 7.1 - Carry out the steps of Computer Problem 1 for the...Ch. 7.1 - Apply the Shooting Method to the nonlinear BVPs....Ch. 7.1 - Carry out the steps of Computer Problem 3 for the...Ch. 7.1 - Prob. 5CP Ch. 7.1 - Verify that (7.10) is a solution of the BVP for...Ch. 7.1 - Set compressibility to the moderate value c=0.01 ....Ch. 7.1 - Prob. 3SA Ch. 7.1 - Change pressure to p=3.5, and resolve the BVP....Ch. 7.1 - Prob. 5SA Ch. 7.1 - Carry out Step 5 for the reduced compressibility...Ch. 7.1 - Carry out Step 5 for increased compressibility...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to plot solutions to the...Ch. 7.2 - (a) Find the solution of the BVP y=y, y(0)=0,...Ch. 7.2 - Solve the nonlinear BVP 4y=ty4, y(1)=2, y(2)=1 by...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Prob. 9CP Ch. 7.2 - Use finite differences to solve the equation {...Ch. 7.2 - Solve { y=cy(1y)y(0)=0y(1/2)=1/4y(1)=1 for c0,...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Carry out the steps of Computer Problem 1, using...Ch. 7.3 - Carry out the steps of Computer Problem 2, using...

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Consider the BVP { y ′ ′ = c y y ( a ) = y a y ( b ) = y b where c > 0 , a < b Show that there exists a unique solution y ( t ) on [ a , b ] . Find a solution of form y ( t ) = c 1 e d 1 t + c 2 e d 2 t for some c 1 , c 2 , d 1 , d 2 .

Solution Summary: The author explains that the given boundary value problem has a unique solution y(t).

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Chapter 7 Solutions

Consider the BVP { y ′ ′ = c y y ( a ) = y a y ( b ) = y b where c &gt; 0 , a &lt; b Show that there exists a unique solution y ( t ) on [ a , b ] . Find a solution of form y ( t ) = c 1 e d 1 t + c 2 e d 2 t for some c 1 , c 2 , d 1 , d 2 .

Solution Summary: The author explains that the given boundary value problem has a unique solution y(t).

Concept explainers

Videos

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Chapter 7 Solutions

Consider the BVP { y ′ ′ = c y y ( a ) = y a y ( b ) = y b where c > 0 , a < b Show that there exists a unique solution y ( t ) on [ a , b ] . Find a solution of form y ( t ) = c 1 e d 1 t + c 2 e d 2 t for some c 1 , c 2 , d 1 , d 2 .