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i = r(1– r²)(4 – r²), é = 2 – r². |

i = r(1– r²)(4 – r²), é = 2 – r². |

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Sketch the phase portrait.

The image presents a system of differential equations in polar coordinates: 1. \(\dot{r} = r(1 - r^2)(4 - r^2)\) 2. \(\dot{\theta} = 2 - r^2\) Explanation: - \(\dot{r}\) represents the radial velocity component, where \(r\) is a function of time. The expression \(r(1 - r^2)(4 - r^2)\) implies that the radial velocity changes with respect to \(r\), influenced by factors such as \(r^2\) and constants. - \(\dot{\theta}\) represents the angular velocity component, where \(\theta\) is a function of time. The expression \(2 - r^2\) indicates that the angular velocity depends on \(r\). There are no graphs or diagrams accompanying the equations.
Transcribed Image Text:The image presents a system of differential equations in polar coordinates: 1. \(\dot{r} = r(1 - r^2)(4 - r^2)\) 2. \(\dot{\theta} = 2 - r^2\) Explanation: - \(\dot{r}\) represents the radial velocity component, where \(r\) is a function of time. The expression \(r(1 - r^2)(4 - r^2)\) implies that the radial velocity changes with respect to \(r\), influenced by factors such as \(r^2\) and constants. - \(\dot{\theta}\) represents the angular velocity component, where \(\theta\) is a function of time. The expression \(2 - r^2\) indicates that the angular velocity depends on \(r\). There are no graphs or diagrams accompanying the equations.
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