Plot the following equation?

Questions
,
1

Hello.

I’d like to plot the equation, y versus x, as shown below.

(4.208*10^-7) (9.98687) y^2/x^2 = 1 - y - ((y^1.58273)/(x^0.58273))

But I’m just a beginner of mathematica, I have no idea to plot this.

And also If there is anybody can arrange that equation for one unknown quantity, y, by using mathematica, please let me know.

Thank you.

2

Hello, I suspect there are no closed-form solutions for this equation. Given admissible X values, however, the corresponding Y values can be determined, as shown in the plot below:

ListLinePlot[
 Table[{x, 
   y /. NSolve[(4.208 10^-7) (9.98687) y^2/x^2 == 
       1 - y - ((y^1.58273)/(x^0.58273)), y, Reals][[1]]}, {x, .1, 20,
    0.1}], AxesLabel -> {"x", "y"}, LabelStyle -> Black]

Which will generate

Untitled.png
Untitled.png360×237 1.49 KB

3

You can use ContourPlot:

ContourPlot[(4.208*10^-7) (9.98687) y^2/x^2 ==
  1 - y - ((y^1.58273)/(x^0.58273)),
 {x, 0, 2}, {y, 0, 1}]

Be careful to use == (equation) and not = (assignment).