Explanation Given: The differential equations are, x ′ = y ( 3 x − 2 ) , y ′ = 2 x − 9 y 2 . Calculation: Consider the given differential equations, x ′ = y ( 3 x − 2 ) , y ′ = 2 x − 9 y 2 . Sketch the phase portrait of the given differential equation for − 2 ≤ x ≤ 2 , − 2 ≤ y ≤ 2 as follows, Figure ( 1 ) From the above sketch of the differential equations, it is clear that the equilibrium point ( 0 , 0 ) is center, ( 2 3 , 2 27 ) , and ( 2 3 , − 2 27 ) are an unstable node

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Author: ANNIN

Publisher: YUZU

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 9.10, Problem 13P

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The phase portrait of the system for −2≤x≤2, −2≤y≤2, and the comment for the types of equilibrium points.

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Chapter 9.10, Problem 12P

Chapter 9.10, Problem 14P

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Chapter 9 Solutions

EBK DIFFERENTIAL EQUATIONS AND LINEAR A

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The phase portrait of the system for − 2 ≤ x ≤ 2 , − 2 ≤ y ≤ 2 , and the comment for the types of equilibrium points.

Solution Summary: The author illustrates the phase portrait of the differential equations for (0,0), and the comment for the types of equilibrium points.

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To sketch:

The phase portrait of the system for −2≤x≤2, −2≤y≤2, and the comment for the types of equilibrium points.

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Chapter 9 Solutions

The phase portrait of the system for − 2 ≤ x ≤ 2 , − 2 ≤ y ≤ 2 , and the comment for the types of equilibrium points.

Solution Summary: The author illustrates the phase portrait of the differential equations for (0,0), and the comment for the types of equilibrium points.

Concept explainers

Videos

To sketch: The phase portrait of the system for −2≤x≤2, −2≤y≤2, and the comment for the types of equilibrium points.

Want to see the full answer?

Chapter 9 Solutions

To sketch:

The phase portrait of the system for −2≤x≤2, −2≤y≤2, and the comment for the types of equilibrium points.