As written it isn't a differential equation as there is no differentiation involved! Have you posted it correctly?
It is posted correctly, I thought I might be able to solve by using a differential equation (didn't mean it was one). Basically I just want to get a function in terms of y (y=...). When I tried to solve it algebraically I got a messy looking equation and still couldn't seem to get y by itself (I got a polynomial function of y's i.e y^2, y^3...). I don't know if it is possible to get y by itself. Basically I want to graph x against y so thats why I want a function in terms of y.
Tricky question?
x=1-[3(1-y)^(2/3)]+2-2y --------(i)
Simplifying that,
x = 3 -2y -3(1-y)^2 -----(ii)
So you only want to solve for "y" in terms of "x" so that you could graph the the equation in the x,y plane?
Why don't you out-trick the original equation then?
In (i) or (ii), swap the x and y,
y =1 -[3(1-x)^(2/3)] +2 -2y --------(ia)
Or,
y = 3 -2x -3(1-x)^2 -----(iia)
1.) Now graph (iia) the usual way.
2.) Then rotate the graph clockwise by 90 dergrees.
The "positive y" now of (iia) will become the real/usual positive x.
But the "positive x" of (iia) will become the real/usual negative y.
3.) So, reverse or flip or rotate this new graph in (2.) about the new, or now real/usual, x-axis by 180 degrees.
The "positive y" now of (iia) will remain as the real/usual positive x.
And the "positive x" of (iia) will become the real/usual positive y.
4.) There now is the graph of x=1-[3(1-y)^(2/3)]+2-2y --------(i).
Sorry, I am not an expert on Excel. I do not even know how to use any graphing calculator or any Math applications like MathLab, MathCad, etc..
I thought you only know how to graph an equation when it is in the form y = ......, that'sa why I suggested what I wrote before.
If you know how to use Excel, you cannot graph the original equation as it is?