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first time using matlab, how can i use solve to find the equilibrium solutions of the differential equation, y` = -( 3 - y ) y

Asked by Mike Randy on 9 Sep 2013

first time using matlab, how can i use solve to find the equilibrium solutions of the differential equation, y` = -( 3 - y ) y

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Mike Randy

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3 Answers

Answer by the cyclist on 9 Sep 2013

I would not use solve(). I would try ode45() to start.

doc ode45

for details and examples.

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the cyclist
Answer by Roger Stafford on 9 Sep 2013

Why bother using matlab when elementary differential equations techniques will easily give the solution:

 y = 3/(1+k*exp(3*x))

for arbitrary constant k and with x the independent variable.

3 Comments

Youssef KHMOU on 10 Sep 2013

Roger, can you add some details about how you obtained the solution ( explaining the variables separation ) because i think it is :

 y=3/(1-k*exp(3*x))
Roger Stafford on 10 Sep 2013

The two forms are entirely equivalent. Your k is the negative of my k. k can be either positive or negative depending on initial conditions.

Roger Stafford
Answer by Youssef KHMOU on 10 Sep 2013

Like @the cylist said, try ode23 or ode45, but you did not mention the initial condition :

 function dy=Myfunction(t,y)
 dy(1)=-(3-y(1)).*y(1);

In the workspace ( initial condition k=0.01 with time [0,,,,10]) :

 >>[t,y]=ode45('Myfunction',0,10,0.010);
 >>plot(t,y)

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Youssef  KHMOU

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