System of Coulped ODE's/ Panic Attack

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Homework Help Overview

The problem involves a system of coupled ordinary differential equations (ODEs) defined by dx/dt = -xy and dy/dt = -xy, with the goal of finding functions x(t) and y(t). The context suggests a focus on analytical methods for solving these equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss integrating the equations and the potential for separating variables. There is a suggestion to solve dy/dt = dx/dt as a preliminary step. Some express uncertainty about the simplicity of the approach and seek further clarification.

Discussion Status

The discussion is ongoing, with various approaches being explored. Some participants have offered steps to take, while others are questioning the assumptions and seeking deeper understanding. There is no explicit consensus on the best method yet.

Contextual Notes

Participants mention difficulties in uncoupling the equations and express frustration over the lack of clear examples in textbooks. There is an emphasis on being cautious with constants during the solution process.

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Homework Statement



dx/dt = -xy

dy/dt =-xy

find x(t) and y(t)


The Attempt at a Solution



Using Maple I've plotted the vector field and solution curve for a list of initial conditions. When I tried to work by hand I could find a way to uncoulple the equations. Is there an analytical solution? Method (linearization and etc. )works best? I've sifted through numerous textbooks and couldn't find a decent example.
 
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As a first step I would integrate dx/dt=dy/dt.
 
Are you telling me its that simple?

Could you go a little further?
 
Last edited:
1st solve dy/dt = dx/dt. You should then be able to solve for y. Next you could plug y into dx/dt = -xy to get a seperable equation. Then solve for x & y. Be careful with your constants!
 
My first thought was that dy/dx= -xy/-xy= 1 but that is precisely what Dick and pki15 are saying.
 

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