Program Explanation Given information: The differential equation is written as, t x ″ + 2 ( t − 1 ) x ′ − 2 x = 0 The initial value of the differential equation is written as, x ( 0 ) = 0 ⇒ x ′ ( 0 ) = 0 Calculation: Apply the Laplace transform on the differential equation and solve as shown below. L { t x ″ + 2 ( t − 1 ) x ′ − 2 x } = L { 0 } − d d s ( L { x ″ ( t ) } ) − 2 d d s ( L { x ′ ( t ) } ) − 2 s L { x ′ ( t ) } − 2 L { x ( t ) } = 0 Use the differential transform theorem and substitute the initial value to solve further as shown below. [ − ( 2 s X ( s ) + s 2 X ′ ( s ) ) + 4 ( X ( s ) + s X ′ ( s ) ) − s X ( s ) − 4 X ′ ( s ) + 2 X ( s ) ] = 0 [ − 2 s X ( s ) − s 2 X ′ ( s ) − 2 X ( s ) − 2 s X ′ ( s ) − 2 s X ( s ) − 2 X ( s ) ] = 0 Further, solve the differential equation as, − ( s 2 + 2 s ) X ′ ( s ) − 4 ( s + 1 ) X ( s ) = 0 − ( s 2 + 2 s ) X ′ ( s ) = 4 ( s + 1 ) X

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Chapter 7.4, Problem 32P

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Program Description: Purpose of problem is to obtain nontrivial solution for the differential equation tx″+2(t−1)x′−2x=0 for the initial condition x(0)=0 .

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Chapter 7.4, Problem 31P

Chapter 7.4, Problem 33P

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Chapter 7 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

Ch. 7.1 - Prob. 11P Ch. 7.1 - Prob. 12P Ch. 7.1 - Prob. 13P Ch. 7.1 - Prob. 14P Ch. 7.1 - Prob. 15P Ch. 7.1 - Prob. 16P Ch. 7.1 - Prob. 17P Ch. 7.1 - Prob. 18P Ch. 7.1 - Prob. 19P Ch. 7.1 - Prob. 20P Ch. 7.1 - Prob. 21P Ch. 7.1 - Prob. 22P Ch. 7.1 - Prob. 23P Ch. 7.1 - Prob. 24P Ch. 7.1 - Prob. 25P Ch. 7.1 - Prob. 26P Ch. 7.1 - Prob. 27P Ch. 7.1 - Prob. 28P Ch. 7.1 - Prob. 29P Ch. 7.1 - Prob. 30P Ch. 7.1 - Prob. 31P Ch. 7.1 - Prob. 32P Ch. 7.1 - Prob. 33P Ch. 7.1 - Prob. 34P Ch. 7.1 - Prob. 35P Ch. 7.1 - Prob. 36P Ch. 7.1 - Given a0, let f(t)=1 if 0__1a,f(t)=0 if t__a....Ch. 7.1 - Given that 0ab. Let f(t)=1 if a__tb,f(t)=0 if...Ch. 7.1 - Prob. 39P Ch. 7.1 - Prob. 40P Ch. 7.1 - Prob. 41P Ch. 7.1 - Given constants a and b. define h(t) for t__0 by...Ch. 7.2 - Prob. 1P Ch. 7.2 - Prob. 2P Ch. 7.2 - Prob. 3P Ch. 7.2 - Prob. 4P Ch. 7.2 - Prob. 5P Ch. 7.2 - Prob. 6P Ch. 7.2 - Prob. 7P Ch. 7.2 - Prob. 8P Ch. 7.2 - Prob. 9P Ch. 7.2 - Prob. 10P Ch. 7.2 - Prob. 11P Ch. 7.2 - Prob. 12P Ch. 7.2 - Prob. 13P Ch. 7.2 - Prob. 14P Ch. 7.2 - Prob. 15P Ch. 7.2 - Prob. 16P Ch. 7.2 - Prob. 17P Ch. 7.2 - Prob. 18P Ch. 7.2 - Prob. 19P Ch. 7.2 - Prob. 20P Ch. 7.2 - Prob. 21P Ch. 7.2 - Prob. 22P Ch. 7.2 - Prob. 23P Ch. 7.2 - Prob. 24P Ch. 7.2 - Prob. 25P Ch. 7.2 - Prob. 26P Ch. 7.2 - Prob. 27P Ch. 7.2 - Prob. 28P Ch. 7.2 - Prob. 29P Ch. 7.2 - Prob. 30P Ch. 7.2 - Prob. 31P Ch. 7.2 - Prob. 32P Ch. 7.2 - Prob. 33P Ch. 7.2 - Prob. 34P Ch. 7.2 - Prob. 35P Ch. 7.2 - Prob. 36P Ch. 7.2 - Prob. 37P Ch. 7.3 - Prob. 1P Ch. 7.3 - Prob. 2P Ch. 7.3 - Prob. 3P Ch. 7.3 - Prob. 4P Ch. 7.3 - Prob. 5P Ch. 7.3 - Prob. 6P Ch. 7.3 - Prob. 7P Ch. 7.3 - Prob. 8P Ch. 7.3 - Prob. 9P Ch. 7.3 - Prob. 10P Ch. 7.3 - Prob. 11P Ch. 7.3 - Prob. 12P Ch. 7.3 - Prob. 13P Ch. 7.3 - Prob. 14P Ch. 7.3 - Prob. 15P Ch. 7.3 - Prob. 16P Ch. 7.3 - Prob. 17P Ch. 7.3 - Prob. 18P Ch. 7.3 - Prob. 19P Ch. 7.3 - Prob. 20P Ch. 7.3 - Prob. 21P Ch. 7.3 - Prob. 22P Ch. 7.3 - Prob. 23P Ch. 7.3 - Prob. 24P Ch. 7.3 - Prob. 25P Ch. 7.3 - Prob. 26P Ch. 7.3 - Prob. 27P Ch. 7.3 - Prob. 28P Ch. 7.3 - Prob. 29P Ch. 7.3 - Prob. 30P Ch. 7.3 - Prob. 31P Ch. 7.3 - Prob. 32P Ch. 7.3 - Prob. 33P Ch. 7.3 - Prob. 34P Ch. 7.3 - Prob. 35P Ch. 7.3 - Prob. 36P Ch. 7.3 - Prob. 37P Ch. 7.3 - Prob. 38P Ch. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.4 - Find the convolution f(t)g(t) in Problems 1...Ch. 7.4 - Prob. 2P Ch. 7.4 - Prob. 3P Ch. 7.4 - Prob. 4P Ch. 7.4 - Prob. 5P Ch. 7.4 - Prob. 6P Ch. 7.4 - Prob. 7P Ch. 7.4 - Prob. 8P Ch. 7.4 - Prob. 9P Ch. 7.4 - Prob. 10P Ch. 7.4 - Prob. 11P Ch. 7.4 - Prob. 12P Ch. 7.4 - Prob. 13P Ch. 7.4 - Prob. 14P Ch. 7.4 - Prob. 15P Ch. 7.4 - Prob. 16P Ch. 7.4 - Prob. 17P Ch. 7.4 - Prob. 18P Ch. 7.4 - Prob. 19P Ch. 7.4 - Prob. 20P Ch. 7.4 - Prob. 21P Ch. 7.4 - Prob. 22P Ch. 7.4 - Prob. 23P Ch. 7.4 - Prob. 24P Ch. 7.4 - Prob. 25P Ch. 7.4 - Prob. 26P Ch. 7.4 - Prob. 27P Ch. 7.4 - Prob. 28P Ch. 7.4 - Prob. 29P Ch. 7.4 - Prob. 30P Ch. 7.4 - Prob. 31P Ch. 7.4 - Prob. 32P Ch. 7.4 - Prob. 33P Ch. 7.4 - Prob. 34P Ch. 7.4 - Prob. 35P Ch. 7.4 - Prob. 36P Ch. 7.4 - Prob. 37P Ch. 7.4 - Prob. 38P Ch. 7.4 - Prob. 39P Ch. 7.4 - Prob. 40P Ch. 7.4 - Prob. 41P Ch. 7.5 - Prob. 1P Ch. 7.5 - Prob. 2P Ch. 7.5 - Prob. 3P Ch. 7.5 - Prob. 4P Ch. 7.5 - Prob. 5P Ch. 7.5 - Prob. 6P Ch. 7.5 - Prob. 7P Ch. 7.5 - Prob. 8P Ch. 7.5 - Prob. 9P Ch. 7.5 - Prob. 10P Ch. 7.5 - Prob. 11P Ch. 7.5 - Prob. 12P Ch. 7.5 - Prob. 13P Ch. 7.5 - Prob. 14P Ch. 7.5 - Prob. 15P Ch. 7.5 - Prob. 16P Ch. 7.5 - Prob. 17P Ch. 7.5 - Prob. 18P Ch. 7.5 - Prob. 19P Ch. 7.5 - Prob. 20P Ch. 7.5 - Prob. 21P Ch. 7.5 - Prob. 22P Ch. 7.5 - Prob. 23P Ch. 7.5 - Prob. 24P Ch. 7.5 - Prob. 25P Ch. 7.5 - Prob. 26P Ch. 7.5 - Let g(t) be the staircase function of Fig. 7.5.15....Ch. 7.5 - Suppose that f(i) is a periodic function of period...Ch. 7.5 - Suppose that f(t) is the half-wave rectification...Ch. 7.5 - Let g(t)=u(tk)f(tk), where f(t) is the function of...Ch. 7.5 - Prob. 31P Ch. 7.5 - Prob. 32P Ch. 7.5 - Prob. 33P Ch. 7.5 - Prob. 34P Ch. 7.5 - Prob. 35P Ch. 7.5 - Prob. 36P Ch. 7.5 - Prob. 37P Ch. 7.5 - Prob. 38P Ch. 7.5 - Prob. 39P Ch. 7.5 - Prob. 40P Ch. 7.5 - Prob. 41P Ch. 7.5 - Prob. 42P Ch. 7.6 - Prob. 1P Ch. 7.6 - Prob. 2P Ch. 7.6 - Prob. 3P Ch. 7.6 - Prob. 4P Ch. 7.6 - Prob. 5P Ch. 7.6 - Prob. 6P Ch. 7.6 - Prob. 7P Ch. 7.6 - Prob. 8P Ch. 7.6 - Prob. 9P Ch. 7.6 - Prob. 10P Ch. 7.6 - Prob. 11P Ch. 7.6 - Prob. 12P Ch. 7.6 - Prob. 13P Ch. 7.6 - Prob. 14P Ch. 7.6 - This problem deals with a mass in on a spring...Ch. 7.6 - Prob. 16P Ch. 7.6 - Prob. 17P Ch. 7.6 - Prob. 18P Ch. 7.6 - Prob. 19P Ch. 7.6 - Repeat Problem 19, except suppose that the switch...Ch. 7.6 - Prob. 21P Ch. 7.6 - Prob. 22P

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Program Description: Purpose of problem is to obtain nontrivial solution for the differential equation t x ″ + 2 ( t − 1 ) x ′ − 2 x = 0 for the initial condition x ( 0 ) = 0 .

Solution Summary: The author explains the purpose of the problem, which is to obtain nontrivial solution for the differential equation.

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Program Description: Purpose of problem is to obtain nontrivial solution for the differential equation tx″+2(t−1)x′−2x=0 for the initial condition x(0)=0 .

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Chapter 7 Solutions