The nonlinear second order differential equation ( 1 + α 2 x 2 ) x ″ + ( β + α 2 ( x ′ ) ) x = 0 has a saddle point at ( 0 , 0 ) when β < 0 .

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Answer 1

Question

Chapter 10.3, Problem 27E

To determine

To show: The nonlinear second order differential equation (1+α2x2)x″+(β+α2(x′))x=0 has a saddle point at (0,0) when β<0.

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Answer 2

Question

Chapter 10.3, Problem 27E

To determine

To show: The nonlinear second order differential equation (1+α2x2)x″+(β+α2(x′))x=0 has a saddle point at (0,0) when β<0.

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Answer 3

Question

Chapter 10.3, Problem 27E

To determine

To show: The nonlinear second order differential equation (1+α2x2)x″+(β+α2(x′))x=0 has a saddle point at (0,0) when β<0.

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Answer 4

Question

Chapter 10.3, Problem 27E

To determine

To show: The nonlinear second order differential equation (1+α2x2)x″+(β+α2(x′))x=0 has a saddle point at (0,0) when β<0.

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Answer 5

Chapter 10.3, Problem 27E

To determine

To show: The nonlinear second order differential equation (1+α2x2)x″+(β+α2(x′))x=0 has a saddle point at (0,0) when β<0.

Answer 6

Chapter 10.3, Problem 27E

To determine

To show: The nonlinear second order differential equation (1+α2x2)x″+(β+α2(x′))x=0 has a saddle point at (0,0) when β<0.

Answer 7

Chapter 10.3, Problem 27E

To determine

To show: The nonlinear second order differential equation (1+α2x2)x″+(β+α2(x′))x=0 has a saddle point at (0,0) when β<0.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 2E Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 4E Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

The nonlinear second order differential equation ( 1 + α 2 x 2 ) x ″ + ( β + α 2 ( x ′ ) ) x = 0 has a saddle point at ( 0 , 0 ) when β < 0 .

Solution Summary: The author explains that the nonlinear second order differential equation (1+alpha)2x 2) has a saddle point.

Concept explainers

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To show: The nonlinear second order differential equation (1+α2x2)x″+(β+α2(x′))x=0 has a saddle point at (0,0) when β<0.

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Chapter 10 Solutions

The nonlinear second order differential equation ( 1 + α 2 x 2 ) x ″ + ( β + α 2 ( x ′ ) ) x = 0 has a saddle point at ( 0 , 0 ) when β &lt; 0 .

Solution Summary: The author explains that the nonlinear second order differential equation (1+alpha)2x 2) has a saddle point.

Concept explainers

Videos

To show: The nonlinear second order differential equation (1+α2x2)x″+(β+α2(x′))x=0 has a saddle point at (0,0) when β<0.

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Chapter 10 Solutions

The nonlinear second order differential equation ( 1 + α 2 x 2 ) x ″ + ( β + α 2 ( x ′ ) ) x = 0 has a saddle point at ( 0 , 0 ) when β < 0 .