Solve the system x’=4x-2xy; y’=-3y+3xy; with initial condition varying in the rectangle [0,7]X[0,7]. Use at least five different points.

Can someone please help me with this, I am new using the program and I really do not know what to do,

[Walter Roberson]

Nasty little system, not very tractable to analysis.

Answer 1

[sixwwwwww]

I will come back to it soon

[Walter Roberson]

No it cannot. The question is about an ODE, so where

x’=4x-2xy

is written in the title, it implies a differential equation

diff(x(t),t) = 4 * x(t) - 2 * x(t) * y(t)

That cannot be solved by using subs().

[sixwwwwww]

Thanks for correction. I forgot to include differential. I recheck it.

[Walter Roberson]

I don't think it can be solved using dsolve() either. Determining the proper constants of integration is difficult, involving integrals that appear to have no closed form, and which cannot be numerically integrated because they go to infinity near x = 0 or y = 0.

[sixwwwwww]

But for different initial conditions we will have different integration constants values. Then it should work

[Walter Roberson]

Even with specific boundary conditions, the integrals along the way have the singularity at x = 0 or y = 0

[sixwwwwww]

Probably you are right it's not easy to solve it directly. Thanks for correction

Answer 2

[Walter Roberson]

Hint: for

x' = 2*x^3 + sin(x)     %random example

you would code

fun = @(x) 2 * x.^3 + sin(x);
ode45(fun, [StartTime, EndTime], [InitialX, InitialY])

such as

ode45(fun, [0 20], [3 7])