(a) Program Explanation Given information: The slope field equation is d y d x = x + y . Explanation: The given equation can be written as, d y d x − y = x The above equation is a linear equation and its solution is obtained as, y e − ∫ d x = ∫ x e − ∫ d x d x y e − x = ∫ x e − x d x Consider the integral ∫ x e − x d x as I and evaluate by parts. u = x ⇒ d u = d x and d v = e − x d x ⇒ v = − e − x The integral I can be written as, ∫ x e x d x = − x e − x − ∫ ( − e (b) Program Plan Intro Program Description: Purpose of problem is to calculate the initial value y 0 so that y ( 5 ) = y 1 .

Pearson eText for Differential Equations: Computing and Modeling Tech Update -- Instant Access (Pearson+)

5th Edition

ISBN: 9780137442782

Author: C. Edwards, David Penney

Publisher: PEARSON+

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Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.

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Chapter 1.5, Problem 44P

(a)

Program Plan Intro

Program Description: Purpose of problem is to show that the solution curve approaches y=−x−1 as x→−∞ .

(b)

Program Plan Intro

Program Description: Purpose of problem is to calculate the initial value y0 so that y(5)=y1 .

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Chapter 1.5, Problem 43P

Chapter 1.5, Problem 45P

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Chapter 1 Solutions

Pearson eText for Differential Equations: Computing and Modeling Tech Update -- Instant Access (Pearson+)

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

Ch. 1.1 - Prob. 11P Ch. 1.1 - Prob. 12P Ch. 1.1 - Prob. 13P Ch. 1.1 - Prob. 14P Ch. 1.1 - Prob. 15P Ch. 1.1 - Prob. 16P Ch. 1.1 - Prob. 17P Ch. 1.1 - Prob. 18P Ch. 1.1 - Prob. 19P Ch. 1.1 - Prob. 20P Ch. 1.1 - Prob. 21P Ch. 1.1 - Prob. 22P Ch. 1.1 - Prob. 23P Ch. 1.1 - Prob. 24P Ch. 1.1 - Prob. 25P Ch. 1.1 - Prob. 26P Ch. 1.1 - Prob. 27P Ch. 1.1 - Prob. 28P Ch. 1.1 - Prob. 29P Ch. 1.1 - Prob. 30P Ch. 1.1 - Prob. 31P Ch. 1.1 - Prob. 32P Ch. 1.1 - Prob. 33P Ch. 1.1 - Prob. 34P Ch. 1.1 - Prob. 35P Ch. 1.1 - Prob. 36P Ch. 1.1 - Prob. 37P Ch. 1.1 - Prob. 38P Ch. 1.1 - Prob. 39P Ch. 1.1 - Prob. 40P Ch. 1.1 - Prob. 41P Ch. 1.1 - Prob. 42P Ch. 1.1 - Prob. 43P Ch. 1.1 - Prob. 44P Ch. 1.1 - Prob. 45P Ch. 1.1 - Prob. 46P Ch. 1.1 - Prob. 47P Ch. 1.1 - Prob. 48P Ch. 1.2 - Prob. 1P Ch. 1.2 - Prob. 2P Ch. 1.2 - Prob. 3P Ch. 1.2 - Prob. 4P Ch. 1.2 - In Problems 1 through 10, find a function y=f(x)...Ch. 1.2 - Prob. 6P Ch. 1.2 - Prob. 7P Ch. 1.2 - Prob. 8P Ch. 1.2 - Prob. 9P Ch. 1.2 - Prob. 10P Ch. 1.2 - Prob. 11P Ch. 1.2 - Prob. 12P Ch. 1.2 - Prob. 13P Ch. 1.2 - Prob. 14P Ch. 1.2 - Prob. 15P Ch. 1.2 - Prob. 16P Ch. 1.2 - Prob. 17P Ch. 1.2 - Prob. 18P Ch. 1.2 - Prob. 19P Ch. 1.2 - Prob. 20P Ch. 1.2 - Prob. 21P Ch. 1.2 - Prob. 22P Ch. 1.2 - Prob. 23P Ch. 1.2 - A ball is dropped from the top of a building 400...Ch. 1.2 - Prob. 25P Ch. 1.2 - Prob. 26P Ch. 1.2 - Prob. 27P Ch. 1.2 - Prob. 28P Ch. 1.2 - A diesel car gradually speeds up so that for the...Ch. 1.2 - Prob. 30P Ch. 1.2 - Prob. 31P Ch. 1.2 - Prob. 32P Ch. 1.2 - On the planet Gzyx, a ball dropped from a height...Ch. 1.2 - Prob. 34P Ch. 1.2 - Prob. 35P Ch. 1.2 - Prob. 36P Ch. 1.2 - Prob. 37P Ch. 1.2 - Prob. 38P Ch. 1.2 - If a=0.5mi and v0=9mi/h as in Example 4, what must...Ch. 1.2 - Prob. 40P Ch. 1.2 - Prob. 41P Ch. 1.2 - Prob. 42P Ch. 1.2 - Prob. 43P Ch. 1.2 - Prob. 44P Ch. 1.3 - Prob. 1P Ch. 1.3 - Prob. 2P Ch. 1.3 - Prob. 3P Ch. 1.3 - Prob. 4P Ch. 1.3 - Prob. 5P Ch. 1.3 - Prob. 6P Ch. 1.3 - Prob. 7P Ch. 1.3 - Prob. 8P Ch. 1.3 - Prob. 9P Ch. 1.3 - Prob. 10P Ch. 1.3 - Prob. 11P Ch. 1.3 - Prob. 12P Ch. 1.3 - Prob. 13P Ch. 1.3 - Prob. 14P Ch. 1.3 - Prob. 15P Ch. 1.3 - Prob. 16P Ch. 1.3 - Prob. 17P Ch. 1.3 - Prob. 18P Ch. 1.3 - Prob. 19P Ch. 1.3 - Prob. 20P Ch. 1.3 - Prob. 21P Ch. 1.3 - Prob. 22P Ch. 1.3 - Prob. 23P Ch. 1.3 - Prob. 24P Ch. 1.3 - Prob. 25P Ch. 1.3 - Prob. 26P Ch. 1.3 - Prob. 27P Ch. 1.3 - Prob. 28P Ch. 1.3 - Verify that if c is a constant, then the function...Ch. 1.3 - Prob. 30P Ch. 1.3 - Prob. 31P Ch. 1.3 - Prob. 32P Ch. 1.3 - Prob. 33P Ch. 1.3 - (a) Use the direction field of Problem 5 to...Ch. 1.3 - Prob. 35P Ch. 1.4 - Prob. 1P Ch. 1.4 - Prob. 2P Ch. 1.4 - Prob. 3P Ch. 1.4 - Prob. 4P Ch. 1.4 - Prob. 5P Ch. 1.4 - Prob. 6P Ch. 1.4 - Prob. 7P Ch. 1.4 - Prob. 8P Ch. 1.4 - Prob. 9P Ch. 1.4 - Prob. 10P Ch. 1.4 - Prob. 11P Ch. 1.4 - Prob. 12P Ch. 1.4 - Prob. 13P Ch. 1.4 - Prob. 14P Ch. 1.4 - Prob. 15P Ch. 1.4 - Prob. 16P Ch. 1.4 - Prob. 17P Ch. 1.4 - Prob. 18P Ch. 1.4 - Prob. 19P Ch. 1.4 - Prob. 20P Ch. 1.4 - Prob. 21P Ch. 1.4 - Prob. 22P Ch. 1.4 - Prob. 23P Ch. 1.4 - Prob. 24P Ch. 1.4 - Prob. 25P Ch. 1.4 - Prob. 26P Ch. 1.4 - Prob. 27P Ch. 1.4 - Prob. 28P Ch. 1.4 - Prob. 29P Ch. 1.4 - Prob. 30P Ch. 1.4 - Prob. 31P Ch. 1.4 - Prob. 32P Ch. 1.4 - (Population growth) A certain city had a...Ch. 1.4 - Prob. 34P Ch. 1.4 - Prob. 35P Ch. 1.4 - (Radiocarbon dating) Carbon taken from a purported...Ch. 1.4 - Prob. 37P Ch. 1.4 - (Continuously compounded interest) Suppose that...Ch. 1.4 - Prob. 39P Ch. 1.4 - Prob. 40P Ch. 1.4 - Prob. 41P Ch. 1.4 - Prob. 42P Ch. 1.4 - Prob. 43P Ch. 1.4 - Prob. 44P Ch. 1.4 - Prob. 45P Ch. 1.4 - Prob. 46P Ch. 1.4 - Prob. 47P Ch. 1.4 - Prob. 48P Ch. 1.4 - Prob. 49P Ch. 1.4 - The amount A (t ) of atmospheric pollutants in a...Ch. 1.4 - An accident at a nuclear power plant has left the...Ch. 1.4 - Prob. 52P Ch. 1.4 - Prob. 53P Ch. 1.4 - Prob. 54P Ch. 1.4 - Prob. 55P Ch. 1.4 - Prob. 56P Ch. 1.4 - Prob. 57P Ch. 1.4 - Prob. 58P Ch. 1.4 - Prob. 59P Ch. 1.4 - Prob. 60P Ch. 1.4 - A spherical tank of radius 4 ft is full of water...Ch. 1.4 - Prob. 62P Ch. 1.4 - Prob. 63P Ch. 1.4 - (The clepsydra, or water clock) A 12 h water clock...Ch. 1.4 - Prob. 65P Ch. 1.4 - Prob. 66P Ch. 1.4 - Prob. 67P Ch. 1.4 - Figure 1.4.11 shows a bead sliding down a...Ch. 1.4 - Prob. 69P Ch. 1.5 - Prob. 1P Ch. 1.5 - Prob. 2P Ch. 1.5 - Prob. 3P Ch. 1.5 - Prob. 4P Ch. 1.5 - Prob. 5P Ch. 1.5 - Prob. 6P Ch. 1.5 - Prob. 7P Ch. 1.5 - Prob. 8P Ch. 1.5 - Prob. 9P Ch. 1.5 - Prob. 10P Ch. 1.5 - Prob. 11P Ch. 1.5 - Prob. 12P Ch. 1.5 - Prob. 13P Ch. 1.5 - Prob. 14P Ch. 1.5 - Prob. 15P Ch. 1.5 - Prob. 16P Ch. 1.5 - Prob. 17P Ch. 1.5 - Prob. 18P Ch. 1.5 - Prob. 19P Ch. 1.5 - Prob. 20P Ch. 1.5 - Prob. 21P Ch. 1.5 - Prob. 22P Ch. 1.5 - Prob. 23P Ch. 1.5 - Prob. 24P Ch. 1.5 - Prob. 25P Ch. 1.5 - Prob. 26P Ch. 1.5 - Prob. 27P Ch. 1.5 - Prob. 28P Ch. 1.5 - Prob. 29P Ch. 1.5 - Prob. 30P Ch. 1.5 - Prob. 31P Ch. 1.5 - Prob. 32P Ch. 1.5 - Prob. 33P Ch. 1.5 - Prob. 34P Ch. 1.5 - Prob. 35P Ch. 1.5 - Prob. 36P Ch. 1.5 - Prob. 37P Ch. 1.5 - Prob. 38P Ch. 1.5 - Prob. 39P Ch. 1.5 - Prob. 40P Ch. 1.5 - Prob. 41P Ch. 1.5 - Prob. 42P Ch. 1.5 - Figure 1.5.7 shows a slope field and typical...Ch. 1.5 - Prob. 44P Ch. 1.5 - Prob. 45P Ch. 1.5 - Prob. 46P Ch. 1.6 - Prob. 1P Ch. 1.6 - Prob. 2P Ch. 1.6 - Prob. 3P Ch. 1.6 - Prob. 4P Ch. 1.6 - Prob. 5P Ch. 1.6 - Prob. 6P Ch. 1.6 - Prob. 7P Ch. 1.6 - Prob. 8P Ch. 1.6 - Prob. 9P Ch. 1.6 - Prob. 10P Ch. 1.6 - Prob. 11P Ch. 1.6 - Prob. 12P Ch. 1.6 - Prob. 13P Ch. 1.6 - Prob. 14P Ch. 1.6 - Prob. 15P Ch. 1.6 - Prob. 16P Ch. 1.6 - Prob. 17P Ch. 1.6 - Prob. 18P Ch. 1.6 - Prob. 19P Ch. 1.6 - Prob. 20P Ch. 1.6 - Prob. 21P Ch. 1.6 - Prob. 22P Ch. 1.6 - Prob. 23P Ch. 1.6 - Prob. 24P Ch. 1.6 - Prob. 25P Ch. 1.6 - Prob. 26P Ch. 1.6 - Prob. 27P Ch. 1.6 - Prob. 28P Ch. 1.6 - Prob. 29P Ch. 1.6 - Prob. 30P Ch. 1.6 - Prob. 31P Ch. 1.6 - Prob. 32P Ch. 1.6 - Prob. 33P Ch. 1.6 - Prob. 34P Ch. 1.6 - Prob. 35P Ch. 1.6 - Prob. 36P Ch. 1.6 - Prob. 37P Ch. 1.6 - Prob. 38P Ch. 1.6 - Prob. 39P Ch. 1.6 - Prob. 40P Ch. 1.6 - Prob. 41P Ch. 1.6 - Prob. 42P Ch. 1.6 - Prob. 43P Ch. 1.6 - Prob. 44P Ch. 1.6 - Prob. 45P Ch. 1.6 - Prob. 46P Ch. 1.6 - Prob. 47P Ch. 1.6 - Prob. 48P Ch. 1.6 - Prob. 49P Ch. 1.6 - Prob. 50P Ch. 1.6 - Prob. 51P Ch. 1.6 - Prob. 52P Ch. 1.6 - Prob. 53P Ch. 1.6 - Prob. 54P Ch. 1.6 - Prob. 55P Ch. 1.6 - Suppose that n0 and n1. Show that the substitution...Ch. 1.6 - Prob. 57P Ch. 1.6 - Prob. 58P Ch. 1.6 - Solve the differential equation dydx=xy1x+y+3 by...Ch. 1.6 - Prob. 60P Ch. 1.6 - Prob. 61P Ch. 1.6 - Prob. 62P Ch. 1.6 - Prob. 63P Ch. 1.6 - Prob. 64P Ch. 1.6 - Prob. 65P Ch. 1.6 - Prob. 66P Ch. 1.6 - Prob. 67P Ch. 1.6 - Prob. 68P Ch. 1.6 - Prob. 69P Ch. 1.6 - As in the text discussion, suppose that an...Ch. 1.6 - Prob. 71P Ch. 1.6 - Prob. 72P Ch. 1 - Prob. 1RP Ch. 1 - Prob. 2RP Ch. 1 - Prob. 3RP Ch. 1 - Prob. 4RP Ch. 1 - Prob. 5RP Ch. 1 - Prob. 6RP Ch. 1 - Prob. 7RP Ch. 1 - Prob. 8RP Ch. 1 - Prob. 9RP Ch. 1 - Prob. 10RP Ch. 1 - Prob. 11RP Ch. 1 - Prob. 12RP Ch. 1 - Prob. 13RP Ch. 1 - Prob. 14RP Ch. 1 - Prob. 15RP Ch. 1 - Prob. 16RP Ch. 1 - Prob. 17RP Ch. 1 - Prob. 18RP Ch. 1 - Prob. 19RP Ch. 1 - Prob. 20RP Ch. 1 - Prob. 21RP Ch. 1 - Prob. 22RP Ch. 1 - Prob. 23RP Ch. 1 - Prob. 24RP Ch. 1 - Prob. 25RP Ch. 1 - Prob. 26RP Ch. 1 - Prob. 27RP Ch. 1 - Prob. 28RP Ch. 1 - Prob. 29RP Ch. 1 - Prob. 30RP Ch. 1 - Prob. 31RP Ch. 1 - Prob. 32RP Ch. 1 - Prob. 33RP Ch. 1 - Prob. 34RP Ch. 1 - Prob. 35RP Ch. 1 - Prob. 36RP

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Program Description: Purpose of problem is to show that the solution curve approaches y = − x − 1 as x → − ∞ .

Solution Summary: The author explains that the solution curve approaches xto -infty . The equation is a linear equation and its solution is obtained by parts.

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Program Description: Purpose of problem is to show that the solution curve approaches y=−x−1 as x→−∞ .

Program Description: Purpose of problem is to calculate the initial value y0 so that y(5)=y1 .

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Chapter 1 Solutions