System of Coulped ODE's/ Panic Attack

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SUMMARY

The discussion focuses on solving a system of coupled ordinary differential equations (ODEs) defined by dx/dt = -xy and dy/dt = -xy. Users explored the use of Maple for plotting vector fields and solution curves, while also seeking analytical solutions. The recommended approach involves first solving dy/dt = dx/dt to isolate y, then substituting y back into the first equation to create a separable equation for x. Attention to constants is crucial in the solution process.

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  • Understanding of coupled ordinary differential equations (ODEs)
  • Familiarity with Maple software for plotting and analysis
  • Knowledge of separation of variables technique in differential equations
  • Basic skills in integration and solving for constants in equations
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  • Learn how to use Maple for solving differential equations
  • Study the method of separation of variables in detail
  • Explore linearization techniques for solving ODEs
  • Review examples of coupled ODEs in advanced mathematics textbooks
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Students and educators in mathematics, particularly those focusing on differential equations, as well as researchers and practitioners using Maple for mathematical modeling and analysis.

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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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