The table for comparing the value of y ( 1.1 ) , y ( 1.2 ) , y ( 1.3 ) , y ( 1.4 ) and y ( 1.5 ) for the differential equation y ′ = x y + y 2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

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Answer 1

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Chapter 9, Problem 4RE

To determine

The table for comparing the value of y(1.1), y(1.2), y(1.3), y(1.4) and y(1.5) for the differential equation y′=xy+y2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

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In Problems 11–20, for the given functions f and g. find: (a) (f° g)(4) (b) (g•f)(2) (c) (fof)(1) (d) (g ° g)(0) \ 11. f(x) = 2x; g(x) = 3x² + 1 12. f(x) = 3x + 2; g(x) = 2x² – 1 1 13. f(x) = 4x² – 3; g(x) = 3 14. f(x) = 2x²; g(x) = 1 – 3x² 15. f(x) = Vx; 8(x) = 2x 16. f(x) = Vx + 1; g(x) = 3x %3D 1. 17. f(x) = |x|; g(x) = 18. f(x) = |x – 2|: g(x) x² + 2 2 x + 1 x² + 1 19. f(x) = 3 8(x) = Vĩ 20. f(x) = x³/2; g(x) = X + 1'

In Problems 2–4, for the given functions fand g find: (a) (f° g) (2) (b) (g • f)(-2) (c) (fo f) (4) (d) (g ° 8) (-1) 2. f(x) = 3x – 5; g(x) = 1 – 2r 3. f(x) = Vx + 2: g(x) = 2x² + 1 4. f(x) = e"; g(x) = 3x – 2

1. Fit the function g(x) = v1x + v2 (x – 1)³ to the data in table below. Xi -1 1 Yi 2 1 -1

Answer 2

Question

Chapter 9, Problem 4RE

To determine

The table for comparing the value of y(1.1), y(1.2), y(1.3), y(1.4) and y(1.5) for the differential equation y′=xy+y2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

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Answer 3

Question

Chapter 9, Problem 4RE

To determine

The table for comparing the value of y(1.1), y(1.2), y(1.3), y(1.4) and y(1.5) for the differential equation y′=xy+y2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

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Answer 4

Question

Chapter 9, Problem 4RE

To determine

The table for comparing the value of y(1.1), y(1.2), y(1.3), y(1.4) and y(1.5) for the differential equation y′=xy+y2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

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Answer 5

Chapter 9, Problem 4RE

To determine

The table for comparing the value of y(1.1), y(1.2), y(1.3), y(1.4) and y(1.5) for the differential equation y′=xy+y2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

Answer 6

Chapter 9, Problem 4RE

To determine

The table for comparing the value of y(1.1), y(1.2), y(1.3), y(1.4) and y(1.5) for the differential equation y′=xy+y2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

Answer 7

Chapter 9, Problem 4RE

To determine

The table for comparing the value of y(1.1), y(1.2), y(1.3), y(1.4) and y(1.5) for the differential equation y′=xy+y2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

Answer 8

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Answer 9

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Answer 10

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Answer 11

The table for comparing the value of y ( 1.1 ) , y ( 1.2 ) , y ( 1.3 ) , y ( 1.4 ) and y ( 1.5 ) for the differential equation y ′ = x y + y 2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

Solution Summary: The author explains the Runga-Kutta method of fourth order and Euler's method.

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The table for comparing the value of y(1.1), y(1.2), y(1.3), y(1.4) and y(1.5) for the differential equation y′=xy+y2 by Euler’s method, Improved Euler’s method and Runga-Kutta method of fourth order.

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