The approximate value of y ( 0.1 ) for the initial value problem y ′ = x − 2 y , y ( 0 ) = 1 .

Question

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Answer 1

Question

Chapter 9.2, Problem 17E

(a)

To determine

The approximate value of y(0.1) for the initial value problem y′=x−2y, y(0)=1.

(b)

To determine

The bound for local truncation error in y1 for the initial value problem y′=x−2y, y(0)=1.

(c)

To determine

The comparison of the error in y1 with obtained error bound in subpart (b).

(d)

To determine

The approximate value of y(0.1) using two steps Euler’s method for the initial value problem y′=x−2y, y(0)=1.

(e)

To determine

The verification of global truncation error for Euler’s method O(h) by comparing the error in parts (a) and (d).

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Answer 2

Question

Chapter 9.2, Problem 17E

(a)

To determine

The approximate value of y(0.1) for the initial value problem y′=x−2y, y(0)=1.

(b)

To determine

The bound for local truncation error in y1 for the initial value problem y′=x−2y, y(0)=1.

(c)

To determine

The comparison of the error in y1 with obtained error bound in subpart (b).

(d)

To determine

The approximate value of y(0.1) using two steps Euler’s method for the initial value problem y′=x−2y, y(0)=1.

(e)

To determine

The verification of global truncation error for Euler’s method O(h) by comparing the error in parts (a) and (d).

Expert Solution & Answer

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See solution

Answer 3

Question

Chapter 9.2, Problem 17E

(a)

To determine

The approximate value of y(0.1) for the initial value problem y′=x−2y, y(0)=1.

(b)

To determine

The bound for local truncation error in y1 for the initial value problem y′=x−2y, y(0)=1.

(c)

To determine

The comparison of the error in y1 with obtained error bound in subpart (b).

(d)

To determine

The approximate value of y(0.1) using two steps Euler’s method for the initial value problem y′=x−2y, y(0)=1.

(e)

To determine

The verification of global truncation error for Euler’s method O(h) by comparing the error in parts (a) and (d).

Expert Solution & Answer

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Answer 4

Question

Chapter 9.2, Problem 17E

(a)

To determine

The approximate value of y(0.1) for the initial value problem y′=x−2y, y(0)=1.

(b)

To determine

The bound for local truncation error in y1 for the initial value problem y′=x−2y, y(0)=1.

(c)

To determine

The comparison of the error in y1 with obtained error bound in subpart (b).

(d)

To determine

The approximate value of y(0.1) using two steps Euler’s method for the initial value problem y′=x−2y, y(0)=1.

(e)

To determine

The verification of global truncation error for Euler’s method O(h) by comparing the error in parts (a) and (d).

Expert Solution & Answer

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Answer 5

Chapter 9.2, Problem 17E

(a)

To determine

The approximate value of y(0.1) for the initial value problem y′=x−2y, y(0)=1.

(b)

To determine

The bound for local truncation error in y1 for the initial value problem y′=x−2y, y(0)=1.

(c)

To determine

The comparison of the error in y1 with obtained error bound in subpart (b).

(d)

To determine

The approximate value of y(0.1) using two steps Euler’s method for the initial value problem y′=x−2y, y(0)=1.

(e)

To determine

The verification of global truncation error for Euler’s method O(h) by comparing the error in parts (a) and (d).

Answer 6

Chapter 9.2, Problem 17E

(a)

To determine

The approximate value of y(0.1) for the initial value problem y′=x−2y, y(0)=1.

Answer 7

Chapter 9.2, Problem 17E

(a)

To determine

The approximate value of y(0.1) for the initial value problem y′=x−2y, y(0)=1.

Answer 8

(b)

To determine

The bound for local truncation error in y1 for the initial value problem y′=x−2y, y(0)=1.

Answer 9

(b)

To determine

The bound for local truncation error in y1 for the initial value problem y′=x−2y, y(0)=1.

Answer 10

(c)

To determine

The comparison of the error in y1 with obtained error bound in subpart (b).

Answer 11

(c)

To determine

The comparison of the error in y1 with obtained error bound in subpart (b).

Answer 12

(d)

To determine

The approximate value of y(0.1) using two steps Euler’s method for the initial value problem y′=x−2y, y(0)=1.

Answer 13

(d)

To determine

The approximate value of y(0.1) using two steps Euler’s method for the initial value problem y′=x−2y, y(0)=1.

Answer 14

(e)

To determine

The verification of global truncation error for Euler’s method O(h) by comparing the error in parts (a) and (d).

Answer 15

(e)

To determine

The verification of global truncation error for Euler’s method O(h) by comparing the error in parts (a) and (d).

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

The approximate value of y ( 0.1 ) for the initial value problem y ′ = x − 2 y , y ( 0 ) = 1 .

Solution Summary: The author explains the approximate value of y(0.1) for the initial value problem.

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The approximate value of y(0.1) for the initial value problem y′=x−2y, y(0)=1.

The bound for local truncation error in y1 for the initial value problem y′=x−2y, y(0)=1.

The comparison of the error in y1 with obtained error bound in subpart (b).

The approximate value of y(0.1) using two steps Euler’s method for the initial value problem y′=x−2y, y(0)=1.

The verification of global truncation error for Euler’s method O(h) by comparing the error in parts (a) and (d).

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Chapter 9 Solutions