Equilibrium Points and Trajectories in the x-xdot Plane

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Homework Help Overview

The discussion revolves around a first-order differential equation expressed in the form dx/dt = x² - 3x - 10. Participants are tasked with finding equilibrium points in the x-xdot plane and drawing trajectories, while also indicating time directions and discussing the nature of the equilibrium points.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the notation differences between dx/dt and xdot, with some questioning the implications of these notations on their understanding of the problem. There is also a discussion about the definitions of velocity and acceleration in relation to xdot and xdotdot.

Discussion Status

Some participants are clarifying their understanding of the notation used in the problem, while others are attempting to connect these concepts to the original task. There is an ongoing exploration of the definitions and relationships between the terms involved.

Contextual Notes

Participants express uncertainty regarding the notation and its implications for solving the problem, indicating a need for clarification on the terms used in the context of differential equations.

franky2727
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ive encountered xdot and x questions before but never one written in this dx/dt format so i don't know what to do?

given the first order differential equation dx/dt=x2 -3x-10 find the equlibrium points in the x--xdot plane and draw the trajectory in the plane indicate the time directions and discuss the natures of the equlibrium points
 
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franky2727 said:
ive encountered xdot and x questions before but never one written in this dx/dt format so i don't know what to do?

If I tell you that dx/dt and \dot x are just different notation for the same thing, can you do it then?
 
i can ye lol, is Xdot just distance in relation to time then?
 
and are you referring to dx/dt=xdot or xdot dot
 
usually xdotdot is acceleration
and xdot is velocity
so xdot: dx/dt
xdotdot : d2x/dt2
 

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