The approximate values of the solution of initial value problem y ′ = 0.5 − t + 2 y , y ( 0 ) = 1 using Euler method with h = 0.1 at t = 0.1 , 0 .2, 0 .3, and 0 .4 .

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Answer 1

Question

Chapter 2.7, Problem 3P

(a)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.1 at t=0.1, 0.2, 0.3, and 0.4.

(b)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.05 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a).

(c)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.025 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a) and part (b).

(d)

To determine

The solution y=ϕ(t) and values of ϕ(t) at t=0.1, 0.2, 0.3, and 0.4. Also compare the results with those obtained in part (a), (b), and (c).

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Answer 2

Question

Chapter 2.7, Problem 3P

(a)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.1 at t=0.1, 0.2, 0.3, and 0.4.

(b)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.05 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a).

(c)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.025 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a) and part (b).

(d)

To determine

The solution y=ϕ(t) and values of ϕ(t) at t=0.1, 0.2, 0.3, and 0.4. Also compare the results with those obtained in part (a), (b), and (c).

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Answer 3

Question

Chapter 2.7, Problem 3P

(a)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.1 at t=0.1, 0.2, 0.3, and 0.4.

(b)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.05 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a).

(c)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.025 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a) and part (b).

(d)

To determine

The solution y=ϕ(t) and values of ϕ(t) at t=0.1, 0.2, 0.3, and 0.4. Also compare the results with those obtained in part (a), (b), and (c).

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Answer 4

Question

Chapter 2.7, Problem 3P

(a)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.1 at t=0.1, 0.2, 0.3, and 0.4.

(b)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.05 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a).

(c)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.025 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a) and part (b).

(d)

To determine

The solution y=ϕ(t) and values of ϕ(t) at t=0.1, 0.2, 0.3, and 0.4. Also compare the results with those obtained in part (a), (b), and (c).

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Answer 5

Chapter 2.7, Problem 3P

(a)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.1 at t=0.1, 0.2, 0.3, and 0.4.

(b)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.05 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a).

(c)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.025 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a) and part (b).

(d)

To determine

The solution y=ϕ(t) and values of ϕ(t) at t=0.1, 0.2, 0.3, and 0.4. Also compare the results with those obtained in part (a), (b), and (c).

Answer 6

Chapter 2.7, Problem 3P

(a)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.1 at t=0.1, 0.2, 0.3, and 0.4.

Answer 7

Chapter 2.7, Problem 3P

(a)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.1 at t=0.1, 0.2, 0.3, and 0.4.

Answer 8

(b)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.05 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a).

Answer 9

(b)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.05 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a).

Answer 10

(c)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.025 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a) and part (b).

Answer 11

(c)

To determine

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.025 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a) and part (b).

Answer 12

(d)

To determine

The solution y=ϕ(t) and values of ϕ(t) at t=0.1, 0.2, 0.3, and 0.4. Also compare the results with those obtained in part (a), (b), and (c).

Answer 13

(d)

To determine

The solution y=ϕ(t) and values of ϕ(t) at t=0.1, 0.2, 0.3, and 0.4. Also compare the results with those obtained in part (a), (b), and (c).

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 2.1 - In each of Problems 1 through 12: Draw a direction...Ch. 2.1 - In each of Problems 1 through 12: Draw a direction...Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - In each of Problems 1 through 12: Draw a direction...Ch. 2.1 - Prob. 8P Ch. 2.1 - Prob. 9P Ch. 2.1 - Prob. 10P

The approximate values of the solution of initial value problem y ′ = 0.5 − t + 2 y , y ( 0 ) = 1 using Euler method with h = 0.1 at t = 0.1 , 0 .2, 0 .3, and 0 .4 .

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The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.1 at t=0.1, 0.2, 0.3, and 0.4.

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.05 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a).

The approximate values of the solution of initial value problem y′=0.5−t+2y, y(0)=1 using Euler method with h=0.025 at t=0.1, 0.2, 0.3, and 0.4 and compare the results with those obtained in part (a) and part (b).

The solution y=ϕ(t) and values of ϕ(t) at t=0.1, 0.2, 0.3, and 0.4. Also compare the results with those obtained in part (a), (b), and (c).

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