# Question:urgent! plot of solutions of differential equations

## Question:urgent! plot of solutions of differential equations

Maple

Hi everyone!

I have an urgent problem!  I am dealing with an autonomous system of 2 differential equations.

First of all I have to plot  the phase plane (x,y) but I'd like to include a constraint (x^2+y^2<1 )in my system and I don't know how to do that!

what I've done by now:

>dfieldplot([diff(x(N),N)=-3*x(N)+sqrt(6)*(y(N))^2+3/2*x(N)*((x(N))^2+1-(y(N))^2), diff(y(N),N)=-sqrt(6)*x(N)*y(N)+3/2*y(N)*((x(N))^2+1-(y(N))^2)],
[x(N),y(N)],N=0..20, x=-1..1, y=0..1, color=black, dirfield=[30,30]);

Then, I'd like to plot on the same graph x as a function of N and also x^2+y^2 as a function of N.

here is what I^ve done to get the plot of x(N):

> f := (x,y) ->-3*x+sqrt(6)*y^2+3/2*x*(x^2+(1-y^2)) ;

> g := (x,y) -> -sqrt(6)*x*y+3/2*y*(x^2+(1-y^2));

> MLV:=[diff(x(N),N)=f(x(N),y(N)), diff(y(N),N) = g(x(N),y(N))];

>ivs:=[[x(0)=0,y(0)=0.01]];

>DEplot(MLV,[x(N),y(N)],N=0..10,ivs,arrows=smalltwo, dirfield=[30,30],color=magnitude[green,red],scene=[N,x(N)]);

Can anyone help me?

Thank you!

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