# Numerically solve equation

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! • Use Rationalize around c and the step size to get rid of the message. Sep 24, 2019 at 8:15 • Reduce[x*(1 - c*x) - x*y/(1 + y^(1 + gamma)) == 0, gamma, Reals] returns what looks like a legitimate solution fairly quickly – gpap Sep 24, 2019 at 8:43 • @user21 This indeed helps to get rid of the method. But I am searching for a solution of some form$x(y,\gamma)\$ and I am only getting ConditionalExpression with this. Any idea? Sep 24, 2019 at 9:01
• @gpap This may be right. But I can't confirm this because I don't know how to plot these expressions.. Any idea on this? Sep 24, 2019 at 9:04
• What's z? Do you mean y? Sep 24, 2019 at 9:13

## 1 Answer

If you're only interested in the plot, not the functional form of x[y, gamma], then you can use ContourPlot3D:

ContourPlot3D[dx == 0, {gamma, 0, 1}, {y, 0, 5}, {x, 0, 1/c},
AxesLabel -> {gamma, y, x}]


• Perfect, thank you. Do you, by chance, know whether/how it is possible to plot only the borders of the surfaces? Sep 24, 2019 at 9:52
• @gumpel Sorry, I don't know about plotting the borders only. Maybe look at ContourPlot3D options. Sep 24, 2019 at 9:59