@acer 

This is great! Thanks a lot!

@vv Thanks!

I didn't know Delta would work without typesetting as well!

@John May Thanks! 

The only problem is that in order to make the plot more clear, I should change the fonts. So I am adding some options and the code is changed to:

p := logplot(x^3, x = 0 .. 2, thickness = 3, font = [bold, "TimesNewRoman", 30], labelfont = [bold, "TimesNewRoman", 30], axis[1] = [thickness = 3], axis[2] = [thickness = 3], axes = boxed); dualaxisplot(p, p)

But surprisingly, the font of the second y-axes does not change!

Could you please help me with that too?

This is the plot I get:

@Kitonum Thanks! 

@John May  great! It's working! thanks!

@rlopez thanks. But it doesn't  work on my maple version either (17)

@Kitonum 

thanks! this works great!

thanks a lot @one man .

Let me say more info that I got:

1- alpha is constant, so if you have it in one point, you have it everywhere.

2- x=x(rho),  y=y(rho),  beta=beta(rho)

3- I know the form of rho

can it be solved not numerically now?

@vv 

unfortunately beta is not an integer.

@Doug Meade 

But, can't I use this value for y everywhere?

BTW, I have no other info.

What else do you think we need? like the order of the parameters? (which I don't also have! :( )

@Doug Meade 

Dear Doug,

This looks like a lot of improvements! Thanks for the help.

Regarding the form of F(a), I tried to use eq3 and also your results for diff(F(a),a). Now I have an equation which only consists of F and a, but I cannot solve it because it takes a lot of time and it does not solve it! I attached the updated worksheet for you.

Also, in the worksheet I saw that for getting y, you used isolate instead of solve. and apparently, you only got one value from the two y values. Could you please explain to me what is the difference between isolate and solve?

differential_eq3.mw

@nidojan 

x and y canbe found solving equations 1 and 2
but the problem is that putting their values in the equation, the differential equation would get so complicated!

you are right about the boundary conditions, it is F(0)=10^(-6)

@tomleslie 

ok so to give you more details, I attach the worksheet.

equations 1 to 3 should be solved for x,y and F(a). But of course to get F(a), we need to sove a differential equation and that is my main problem.

differential_eq.mw

@Preben Alsholm 

I just found out the problem!

When exporting, I saved it as "font_size.mpl"

However, I should have saved it as "font_size"!!! without the extension!

@acer 

You are right. This has not been pasted well!

So the right one is:

densityplot(x*exp(−x^2−y^2),x=−2..2,y=−2..2,colorscheme=["𝙱𝚕𝚞𝚎","𝙶𝚛𝚎𝚎𝚗","𝙾𝚛𝚊𝚗𝚐𝚎"])

Anyway, it gives me the same error: 

Error, (in plot/options2d) unexpected option: colorscheme = ["Blue", "Green", "Orange"]

using your code with the styleoption it gives me:

Error, (in plots/densityplot) incorrect style option

I am using maple 17 (2013).

Can this be the reason?!