I have an equation, that I want to solve numerically. The equation is
$$x(1-cx)-\frac{xy}{1+x^{1+\gamma}}=0$$
The problem here is the $\gamma$. What I want to achieve is a plot of the solutions in the $(x,y,\gamma)$-space. Actually, I want to plot ther borders of the surface, to make the other surfaces visible as well, but this is another issue. I have a fixed value of $c$ and I realized, that symbolically, this would get quite hard. So my first approach was something like this:
$Assumptions = gamma >= 0 && x>=0 && z>=0;
c = 0.1732;
dx := x*(1 - c*x) - x*y/(1 + y^(1 + gamma))
Reap[Do[Sow[NSolve[dx==0,p,Reals]],{gamma,0,1,0.05}]]
I get the following error
NSolve was unable to solve the system with inexact coefficients.
Isn't there a simple solution to obtain all positive real solutions for $x$, assuming that $y>= 0$?
Thank you!
Rationalizearoundcand the step size to get rid of the message. $\endgroup$ – user21 Sep 24 at 8:15Reduce[x*(1 - c*x) - x*y/(1 + y^(1 + gamma)) == 0, gamma, Reals]returns what looks like a legitimate solution fairly quickly $\endgroup$ – gpap Sep 24 at 8:43ConditionalExpressionwith this. Any idea? $\endgroup$ – gumpel Sep 24 at 9:01z? Do you meany? $\endgroup$ – Chris K Sep 24 at 9:13