@acer 

Interesting, but al that do and don't  makes it not really easy.
Is it not possible in a "next level" of programming to simplify this ? 
In general ask myself can Maple be programmed to a higher level of user-friendlyness ?

Its a Achimedean Solid this regular tetrahedron ?
For someone who wants to learn the geom3d  package better  its a useful example 

See also https://www.mapleprimes.com/questions/230162-Calculating-Area-Of-Shadow-#answer271424

ode:=diff(f(x),x)=f(x)^(-1);
dsolve(ode);
                                   d          1  
                           ode := --- f(x) = ----
                                   dx        f(x)
                                (1/2)                     (1/2)
              f(x) = (2 x + _C1)     , f(x) = -(2 x + _C1)     

@janhardo 

@Carl Love 

Thanks

Well , i don't see it , thats why i could not figured out by meself

@nm 

Thanks

You are right for this type of ODE its solved by integrating and rather easy to solve. 

@vv 

Thanks

Yes, indeed its not function with multiplicative inverse., but a inverse function see 

https://en.wikipedia.org/wiki/Inverse_function

@nm 

Thanks

Just annother last question :how do you get the blue answers between the gray boxes ?  

@acer 

Thanks

Yes, i tried that first with the <pre> tags( no <quote> tags) ( made in past some websites , so tags were familiar) 
But get not the text between the two tags.
There were two  <P>  lines and the blocks get separated 
Tried several times and gave up too soon.

@nm 

DEtools['odeadvisor']( y(x) = 1*ln(cos(diff(y(x), x)))+(diff(y(x), x))*tan(diff(y(x), x)), y(x), 'help' );
                          [_dAlembert]
----------------------------------
DEtools['odeadvisor']( y(x) = ln(cos(diff(y(x), x)))+(diff(y(x), x))*tan(diff(y(x), x)), y(x), 'help' );
                          [_dAlembert]

For x= 1 you get a dAlembert ODE

@Carl Love 

Thanks

Now i can make a gray box  ( distracted by the two A's )

@nm 

Thanks

I overlooked this icon.

@nm 

In this form how can the x be vanished ? 

y = x*f(p) + g(p)   

Only if  f(p) = 0 , because x . 0 = 0 
y = 0 + g(p) 
y = g(y')   ( p = dy/dx)  is this still a d'Alembert ( Maple say yes ..no quadrature) 
and g is function

For x= 1 you get  y = 1. f(p)+g(p)  d'Alembert ODE
For x= 0 you get a quadrature ODE

 

@vv 

Well, at least with the odeadvisor you know if you are dealing with a standard form or variant of a particular ODE  

@Preben Alsholm 

Thanks!

Works good now.
As you instructed.  
 

Thanks

What i do sometimes for learning a new program is looking how the F1..  keys are assigned in menu or in general.
In maple menu its hidden : its under <edit>split or join that F3 and F4 are explained + Shift F3....

That's not handy done in Maple !.. i like t see in the menu right away the F3 and F4 etc 
Also i like to see in Maple in a save folder ( same as in Microsoft Windows 10)  that i can copy en save,delete worksheets.
And also naming worksheets inthe save folder of Maple : same as in Microsoft Windows 10)
That were some sidenotes and maybe it will be chanced in Maple in the near future. 

I split the regions and the de command is working, that's good, but a error message still exists : Error, unexpected single forward quote. .some text is causes this