DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS

3rd Edition

ISBN: 9781119764564

Author: BRANNAN

Publisher: WILEY

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Textbook Question

Chapter 4.7, Problem 37P

Use the result of Problem 33 to find the solution of the initial value problem

$L [ y ] = ( D − a ) 2 y = g ( t )$ ,

$y ( t 0 ) = 0 , y ' ( t 0 ) = 0$ ,

where $a$ is any real number.

33. By choosing the lower limit of integration in Eq. (27) in the text as the initial point $t 0$ , show that $Y ( t )$ becomes

$Y ( t ) = ∫ t 0 t y 1 ( τ ) y 2 ( t ) − y 1 ( t ) y 2 ( τ ) y 1 ( τ ) y 2 ' ( τ ) − y 1 ' ( τ ) y 2 ( τ ) g ( τ ) d τ$

Show that $Y ( t )$ is a solution of the initial value problem

$L [ y ] = g ( t )$ , $y ( t 0 ) = 0$ , $y ' ( t 0 ) = 0$

Thus $Y$ can be identified with $v$ in problem 32.

$Y ( t ) = − y 1 ( t ) ∫ y 2 ( t ) g ( t ) W [ y 1 , y 2 ] ( t ) d t + y 2 ( t ) ∫ y 1 ( t ) g ( t ) W [ y 1 , y 2 ] ( t ) d t$ (27)

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Chapter 4.7, Problem 36P

Chapter 4.7, Problem 38P

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Chapter 4 Solutions

DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS

Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - A mass weighing stretches a spring . What is the...Ch. 4.1 - A mass attached to a vertical spring is slowly...Ch. 4.1 - A mass weighing stretches a spring . The mass is...

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