Knowing the realations between cartesian ans shperoidal coordinates (x,y,z and v,u,w respectively)

the goal is to take the following graph:

This graphic consists of three planes (One with v=const, let's say v=2, the other one with u=const, let's say u=π/4 and the last one with w=const let's say w=π/4), of three coordinate lines (line v with u=π/4 and w=π/4, line u with v=2 and w=π/4 and finally line w with v=2 and u=π/4). I wrote the following code but an error occurs...

restart;
with(plots);
with(LinearAlgebra);
F := <2*cosh(1)*cos(x), 2*sinh(1)*sin(x)*sin(t), 2*sinh(1)*sin(x)*cos(t)>;
S1 := plot3d(F, x = -Pi/2 .. Pi/2, t = 0 .. 2*Pi, color = "Green");
F, 1.5*Normalize(diff(F, x), 2);
eval(%, {t = Pi/4, x = Pi/4});
A1 := arrow(%, color = red);
V1 := textplot3d(<`+`(`%%`), v^`0`>, align = {'above', 'right'}, font = [Roman, bold, 14]);
F, 1.5*Normalize(diff(F, t), 2);
eval(%, {t = Pi/4, x = Pi/4});
A2 := arrow(%, color = red);
V2 := textplot3d(<`+`(`%%`), u^`0`>, align = {'below'}, font = [Roman, bold, 14]);
G := <2*cosh(x)*cos(Pi/4), 2*sinh(x)*sin(Pi/4)*sin(t), 2*sinh(x)*sin(Pi/4)*cos(t)>;
S2 := plot3d(G, x = 0 .. 100, t = 0 .. 2*Pi, color = "Cyan");
G, 1.5*Normalize(diff(G, x), 2);
eval(%, {t = Pi/4, x = Pi/4});
A3 := arrow(%, color = red);
V3 := textplot3d(<`+`(`%%`), w^`0`>, align = {'above', 'left'}, font = [Roman, bold, 14]);
display(S1, S2, A1, A2, A3, V1, V2, V3, scaling = constrained, axes = framed, labels = [x, y, z]);
 

Given an expression, I want to obtain list of all functions in it, that contains as argument, anywhere another function.  

I can do this now using 2 steps. I was wondering if there is a way to do it in one call.

Here is an example.

expr:=sin(x)+ln(abs(x))+ln(x+1/sqrt(abs(x+3)))+ln(x^3);

The goal is to find all ln functions, with abs inside them. Now, I do this

restart;
expr:=sin(x)+ln(abs(x))+ln(x+1/sqrt(abs(x+3)))+ln(x^3);
lis:=indets(expr,'specfunc(anything,ln)');
select(Z->has(Z,abs),lis)

I could not find a way to do it in one call, If I do this

indets(expr,'specfunc(abs(anything),ln)');

it only finds

Which overlooked the other one, since abs there is elsewhere in side ln.

I looked at help Definition of a Structured Type in Maple but do not know yet if there is an option there to do this. 

Is it possible to do this on one call?  Just wondering, that is all. The above works OK for me now.

Maple 2020.2

How I can edit and apply the following conditions to my plot functions 

`######   I want to change q  (starting from 0.3) from 0.3 by .001 to 0.377 and plot 2D (u-q) ,(v,q), (u,v) and  plot3D (u,v,q)`

`######   I want to change q (starting from 0.37727) from 0.37727 by .001 to 0.390059 and h from 0.1 by .001 to 0.138462  and plot 2D (h-q)  and  plot3D (u,h,q),(v,h,q)`

I couldn't attach my file here, so I uploaded that here

https://drive.google.com/file/d/17purRxEdDqrTJeFDcF1-d9J7b3LkuJnF/view?usp=sharing

I just got a "new" graphics card, NVIDIA GT630, and was wondering whether the CUDA capabilities are accessible. But no luck:

CUDA:-Enable();

Error, (in CUDA:-Enable) CUDA not supported on the current system (see CUDA,supported_hardware for more information)

The CUDA help page with the example, when run, just shows a host of error messages.

I have OS X 10.11.6, the above mentioned GT630 card with claimed 384 CUDA cores and 2 GB of VRAM; NVIDIA WebDriver 346.03.15f16 for the card (i.e. latest for this OS) and NVIDIA CUDA driver 8.0.90 (again, latest for this OS as far as I can tell). My Maple is 2015.2. All this running on a MacPro 4,1.

I am not having great illusions about the performance I should get (this is not a state-of-the-art card today), but it seems to me this combination should be working with Maple 2015 and not throw an error, shouldn't it? Checking the system extensions: CUDA.kext is loaded and its dependencies are satisfied, so I don't see any problem there.

Am I missing something?

M.D.

We have the equation of the following plane in the three-dimension space :

with m1=10, m2=2, C=20 and r1 and r2 given by the following expressions:

with d1=0.6 and d2=0.4. How can we get in Maple the graph of this equation on the x0y plane (z=0) ?

I'm having an issue with Maple 2020.2 classic interface being *very* slow on a new MacBook pro with Big Sur. It takes about 1 second between each keystroke and it appearing on the screen. 

Is this a known bug?

the problem is (FROBENIUS METHOD)
Determine the singular points and identify which of these points are regular points

x(x²-9)² y'' + (x+3) y' +5y = 0

can anyone show me how to do it in maple?  thank you. 

Hi. i have a nonlinear integral equation. any idea for solving it? tnx in advance

integral-equation.mw

restart;
with(Syrup);
ckt := "*\n\
V1 1 0 -10*exp(-2*t)\n\
R1 1 2 2\n\
R2 2 3 2\n\
C1 3 0 0.5F\n\
R3 2 4 4\n\
L1 4 3 1H\n\
.end";
volts,others:=Solve(ckt,'tran', 'returnall'):

How do I get an expression for diff(i1(t),t)?    I tried

eval(diff(i[R1](t),t), volts union others);
But, this looks very strange

diff(i2(t),t)?  I tried a similar expression, but, it is ver different than the one by OP.

How do I set the initial conditions?  I can use init=1, on L1 for i2(0)=1.  But, how about i1(0)=1?

I could not create a 50 X 17 matrix, part of a multiple linear regression exercise & received the message:

"error in (Matrix) too many patterns for typematch". This appears to be an undocumented message in the help page.

I was using the DirectSearch:-GlobalSearch function on a LaguerrelL for values of 4 and 5. At a value of 4 I get a solution, but at 5 I get an error message that the Kernel connection is lost. I ran this script on two different PCs using Maple 2019 and 2020 with WIN 10 and get the same results. Why does this happen?

Here is my worksheet. Thanks for looking.

mysearch2.mw

Hi,

I am studying nonlinear differential equations, and came across an interesting one on maple's help page.  I made a post about this equation already, but I have decided to make a new post because the topic is slightly different than from the previous post.

The topic of this post is:

"Can numerical methods and exact, implicit techniques find false solutions?"

To make the discussion clearer, the rest of this post can be found in the maple file I created.

Download analy_numer.mw

Hello,
I am trying to compute the convolution integral numerically and compare the result with the analytic result. My numerics is giving terrible results:

Is there one place which summarizes major difference between using solve vs. PDEtools:-Solve to solve equation? (ofcourse can one read help for both commands, and try to figure the differences this way, but this is not as easy as it sounds. I was looking more for a short basic summary type list. So I am making one myself in my maple cheat sheet).

I am trying to switch to PDEtools:-Solve from solve, but I keep noticing strange differences. Here is an example

example A

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x));
check:=odetest(sol,ode);
PDEtools:-Solve(check=0,x) assuming x>-1,x<6

Error, (in assuming) when calling 'PDEtools:-Solve'. Received: 'not a system with respect to the unknowns {x}'

Compare to 

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x));
check:=odetest(sol,ode);
solve(check=0,x) assuming x>-1,x<6;

                               x

Now, back to first example above using Solve. I moved the assuming inside, and now the error went away

Example B

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x));
check:=odetest(sol,ode);
PDEtools:-Solve(check=0,x,assume=[x>-1,x<6]);

But I noticed I can not do the same with solve. i.e. move the assuming inside solve, it now gives an error

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x));
check:=odetest(sol,ode);
solve(check=0,x,assume=[x>-1,x<6]);

Error, invalid input: too many and/or wrong type of arguments passed to solve; first unused argument is assume = [-1 < x, x < 6]

So first difference is that one can use assume= inside Solve, but not inside solve. Which is fine.

But I still not sure why first example A above gives error with Solve but not with solve. Any idea why that is?  Notice that example A gives an error with Solve, only when adding x<6 to the assumption. So this works

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x));
check:=odetest(sol,ode);
PDEtools:-Solve(check=0,x) assuming x>-1

No error, and now it gives

But was trying to find why it failed when adding x<6

Maple 2020.2 on windows 10.

This ode

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x))

Direct use of odetest does not give zero.

res:=odetest(sol,ode)

When asking Solve for possible values of x which makes the above zero, it only gave the upper bound

PDEtools:-Solve(res=0,x)

The actual range which makes res=0 is actually -1<x<exp(2)-1

res:=odetest(sol,ode) assuming -1<x,x<exp(2)-1

How could one using Maple obtain this range -1<x<exp(2)-1? 

Mathematica gives the answer using Reduce:

res=Log[Sqrt[x+1]]-1+Sign[Log[(x+1)]-2]*Log[Sqrt[x+1]]-Sign[Log[x+1]-2];
Reduce[res==0,x,Reals]

Is it possible to obtain such result in Maple, since Solve did not give complete answer.

Maple 2020.2