# How to plot different dependent varaibles against the same independent variable

Let's say I have a dispersion relation $$\omega=\exp{k}$$, how should I write a mathematica code to ask for plots of $$\omega$$ against $$k$$ as well as the phase speed $$\omega/k$$ against $$k$$ for a range of $$k\in(-10,10)$$ and $$\omega/k\in(-5,5)$$?

I tried to write my code as follows:

ContourPlot[Dis==0,{k,-10,10},{\[Omega],-5k,5k}]


And this worked, a graph is plotted successfully. Here Dis is defined as Dis = $$\omega-\exp{k}$$.

However, when I try plotting phase speed against wavenumber, a graph cannot be plotted. My code is as follows

a=\[Omega]/k
ContourPlot[Dis==0,{k,-10,10},{a,-5,5}]


• Why do you want to use "ContourPlot"? I think "Plot" will do: Plot[{Exp[k], Exp[k]/k}, {k, -10, 10}] Commented Oct 27, 2021 at 8:52

Clear[dis,reg];
dis = ω - E^k;
reg = ParametricRegion[{{k, a},
dis == 0 && a == ω/k}, {{k, -10, 10}, ω, {a, -5,
5}}];
RegionPlot[reg, PlotRange -> {{-10, 10}, {-5, 5}},
FrameLabel -> {"k", "a"}, LabelStyle -> Directive[Blue, Bold, 12]]
(*Region[reg]*)


We can also test another cases, for example:

dis = k*(ω^2 + ω) - E^k;