Like this?  If so, see the help files for parametric plotting.

>plot([1+x*(2*x^2 +3)^(1/2),x^2,x=0..5]);

>?plot[parametric]

Start with the help files for the VariationalCalculus package.  There you will find a command to construct the Euler-Lagrange equations.  The command below will take you to the help file directly.

?VariationalCalculus[EulerLagrange]

Take a look at the help files for the odeplot command.

?odeplot

>restart: with(plots): with(DEtools):

>ode := diff(phi(z), z, z, z)+(diff(phi(z), z, z))*phi(z) = 0:
>ics := phi(0) = 0, (D[1](phi))(0) = 0, (D[1, 1](phi))(0) = 1:
>ans := dsolve({ics, ode}, numeric, phi(z), range = 0 .. 100):

>odeplot(ans,[z,phi(z)],0..10,style=point);

You can remove the style=point to see a solid line.
 

Does the plot agree with your expectations?

You can also do this with DEplot directly (DEtools) needs to be loaded.

>DEplot( ode, phi(z),z=0..10,[[phi(0) = 0, (D[1](phi))(0) = 0, (D[1, 1](phi))(0) = 1]] );

Regards,
Georgios Kokovidis

Try the following.

plot(rhsarr);

If this works for you, the points will be connected by a line.  If you want points, then you can use the "style" option.

plot(rhsarr,style=point);

If this does not work, can you upload your complete worksheet that generated these points.

I'm not seeing your error with the code that you posted.  I notice that you are multiplying very large and very small numbers.  This might cause round-off errors.  When I increase the number of digits, Maple will not return an answer.  Otherwise Maple returns 0.  I get the same results with Maple 9.51 and Maple 12.

Download 221_integral.mws
View file details

You might want to recreate your plot using the amimate3d command.  Then you can use the frames option.  By default, the number of frames is set to 8.  You can increase this to slow down the animation.  See the example below with and without the frames option.  If this works, then you can export it using your method above and see what happens to your gif.

restart: with(plots):

animate3d(sin(x+t)*cos(y-t),x=0..2*Pi,y=0..2*Pi,t=0..Pi);

animate3d(sin(x+t)*cos(y-t),x=0..2*Pi,y=0..2*Pi,t=0..Pi,frames=50);

For some reason, I thought that the procedure was being echoed because of the semicolon.  I was mistaken.  I was using the Standard GUI, which is why it worked for me.

 The last line of the procedure that Robert Israel provided ends like this:

end proc;

Change the semicolon to a colon.

end proc:

and try executing the code again.  It should work fine.

 

The help pages for dsolve have a description of how this is done.  Take a look at the help page that describes error control.  At the prompt, type the folowing and hti the enter key.  This is a good starting point, although by no means is it exhaustive.

?dsolve,Error_Control

At the Maple prompt, type the following and hit the enter key,
or do a search in the help pages.

?NewtonsMethod

You will see many examples.  Try them.  Then use your function
and see what happens.  Because this function has more than one
answer, depending on where your starting value is, you might 
want to plot it, and then try different starting values to see
what solution you come up with.

plot(4*cos(x)-0.9*x,x);
  

The integration tutor will not show you this.  And even if it did, it might not be what you would have chosen if you did it by hand step by step.  My advice would be to use it as a verification of your answer, or as an aid, but do not use it to guide you step by step.  Working through the problems in a standard calculus text by hand is the best way to learn how to do this, and ultimately to gain experience and insight as to how to choose the u-substitution variable on your own.  As an example, you might try the integration tutuor with this problem:

sqrt(2*x-1)

When asked for the next step, it chooses u^2 after substitution. This is correct, but there are steps ommited.   When doing this by hand, my choice would be to let u=2*x-1, and then du=2dx.  At the end, you will get the same answer.  The only thing I am pointing out is that your choice of substitution variables might not be Maple's choice.  Either way, practice by hand with many many problems is the best way to learn.

restart:

x:=(u,v)->cos(v);
y:=(u,v)->sin(v);
z:=(u,v)->u;

plot3d([x(u,v),y(u,v),z(u,v)],u = 0..30, v = 0..2*Pi,axes=boxed);

This will display a cylinder.  Is this what you want?

>B :=  map(diff,A,x);

The orientation command is available in Maple v8.  I checked the user guide.  The  first value is theta and the second is phi.  As Alex mentioned above, when you left click on the graph and rotate, check the upper left hand side of the toolbar, right under the file menu.  You should see those values change as you rotate.  I checked in v9 and it works the same way.  I do not have v8 loaded, but I know that the commands are supported.

with(DEtools):
ODE:=R(r)+ r*diff(R(r),r)+r^2*diff(R(r),r,r)=0;

ODE := R(r)+r*diff(R(r),r)+r^2*diff(R(r),`$`(r,2)) = 0

odeadvisor(ODE);

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]