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

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

Answer 1

[the cyclist]

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

doc ode45

for details and examples.

Answer 2

[Roger Stafford]

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.

[Youssef Khmou]

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]

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.

[Youssef Khmou]

OK

Answer 3

[Youssef Khmou]

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)