The solution for the differential equation y ′ = x 2 − y 2 with initial condition y ( 0 ) = 1 in direction field and estimate the value of y ( 0.3 ) from the graph.

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Answer 1

Question

Chapter 9, Problem 3RE

(a)

To determine

To sketch: The solution for the differential equation y′=x2−y2 with initial condition y(0)=1 in direction field and estimate the value of y(0.3) from the graph.

(b)

To determine

To estimate: The value of y(0.3) using Euler’s method with step size 0.1 and compare the result from part (a).

(c)

To determine

To find: The lines which are the centers of the horizontal line segments of the direction field in part (a).

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Answer 2

Question

Chapter 9, Problem 3RE

(a)

To determine

To sketch: The solution for the differential equation y′=x2−y2 with initial condition y(0)=1 in direction field and estimate the value of y(0.3) from the graph.

(b)

To determine

To estimate: The value of y(0.3) using Euler’s method with step size 0.1 and compare the result from part (a).

(c)

To determine

To find: The lines which are the centers of the horizontal line segments of the direction field in part (a).

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Answer 3

Question

Chapter 9, Problem 3RE

(a)

To determine

To sketch: The solution for the differential equation y′=x2−y2 with initial condition y(0)=1 in direction field and estimate the value of y(0.3) from the graph.

(b)

To determine

To estimate: The value of y(0.3) using Euler’s method with step size 0.1 and compare the result from part (a).

(c)

To determine

To find: The lines which are the centers of the horizontal line segments of the direction field in part (a).

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Answer 4

Question

Chapter 9, Problem 3RE

(a)

To determine

To sketch: The solution for the differential equation y′=x2−y2 with initial condition y(0)=1 in direction field and estimate the value of y(0.3) from the graph.

(b)

To determine

To estimate: The value of y(0.3) using Euler’s method with step size 0.1 and compare the result from part (a).

(c)

To determine

To find: The lines which are the centers of the horizontal line segments of the direction field in part (a).

Expert Solution & Answer

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Answer 5

Chapter 9, Problem 3RE

(a)

To determine

To sketch: The solution for the differential equation y′=x2−y2 with initial condition y(0)=1 in direction field and estimate the value of y(0.3) from the graph.

(b)

To determine

To estimate: The value of y(0.3) using Euler’s method with step size 0.1 and compare the result from part (a).

(c)

To determine

To find: The lines which are the centers of the horizontal line segments of the direction field in part (a).

Answer 6

Chapter 9, Problem 3RE

(a)

To determine

To sketch: The solution for the differential equation y′=x2−y2 with initial condition y(0)=1 in direction field and estimate the value of y(0.3) from the graph.

Answer 7

Chapter 9, Problem 3RE

(a)

To determine

To sketch: The solution for the differential equation y′=x2−y2 with initial condition y(0)=1 in direction field and estimate the value of y(0.3) from the graph.

Answer 8

(b)

To determine

To estimate: The value of y(0.3) using Euler’s method with step size 0.1 and compare the result from part (a).

Answer 9

(b)

To determine

To estimate: The value of y(0.3) using Euler’s method with step size 0.1 and compare the result from part (a).

Answer 10

(c)

To determine

To find: The lines which are the centers of the horizontal line segments of the direction field in part (a).

Answer 11

(c)

To determine

To find: The lines which are the centers of the horizontal line segments of the direction field in part (a).

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 9.1 - Show that y=23ex+e2x is a solution of the...Ch. 9.1 - Prob. 2E Ch. 9.1 - (a) For what values of r does the function y = erx...Ch. 9.1 - (a) For what values of k does the function y = cos...Ch. 9.1 - Which of the following functions are solutions of...Ch. 9.1 - (a) Show that every member of the family of...Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

The solution for the differential equation y ′ = x 2 − y 2 with initial condition y ( 0 ) = 1 in direction field and estimate the value of y ( 0.3 ) from the graph.

Solution Summary: The author illustrates the solution of the differential equation yprime with its initial condition and estimates its value from the graph using Euler's method.

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To sketch: The solution for the differential equation y′=x2−y2 with initial condition y(0)=1 in direction field and estimate the value of y(0.3) from the graph.

To estimate: The value of y(0.3) using Euler’s method with step size 0.1 and compare the result from part (a).

To find: The lines which are the centers of the horizontal line segments of the direction field in part (a).

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Chapter 9 Solutions