## write finite  boundary conditions in dsolve?? ...

how i can write these boundary conditions for dsolve?

(diff(u(r), r))^(n-1)*(diff(r*(diff(u(r), r)), r))/r    be [finite] at r =0

and  u(0) = finite?

Thanks..

## Using Physics inside a procedure...

Hello!

I can't seem to figure out how to use the Physics package within a procedure. In particular, I can't get tensors to be recognized within the body of the proc.

As an example, here's a short program that works correctly when not in a procedure:

```with(Physics):
Coordinates(X,quiet):
d_[mu](X[~mu]);
# Returns 4; Correct```

However, placing this code inside a proc causes the tensor X to not be recognized as a tensor:

```Test := proc()
uses Physics:

Coordinates(X,quiet):
d_[mu](X[~mu]);
end proc:
Test();
# Returns 0; Wrong```

Apparently, Physics:-Coordinates still defines the tensor X (as can be checked by calling Physics:-Define()). However, the derivative d_[mu] (X[~mu]) seems to be treating X as a standard symbol. Any idea how I would go about correcting this?

Thanks!

## Odditity in CircleSum Procedure...

I have a procedure which works. &oplus;(a,b) gives annwer.   a &oplus; b also gives answer. That was a surprise, discovered from a typing mistake. If b is negative is needs to be enclosed in delay evulation quotes.

2  questions

Can anyoone expllain this useful property? Any way around having to use delay evaluation quotes for negative numbers?

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## How to obtain the Version number of the Physics pa...

On the maple cloud, I see that current version is 38 for Physics

After I installed, I typed

Physics:-Version();

It gives

I was expecting to see "38".  Why does Physics:-Version(); does not give the version number as shown on Maple cloud? Using only a date for a version number is not a good idea. There should be a number there. (date can also be included, but a number should be the official version number).

Is there another command to use to obtain Version number "38"?

Does each package shown on cloud support packageName:-Version()? I tried this command on another package I have, but I got an error saying it does not Version()

OrthogonalExpansions:-Version();
Error, Version is not a command in the OrthogonalExpansions package

Yet, on cloud, it says the version number is "1" for the above package. What does the version number shown on the cloud then really mean?

## pdsolve: PDE by series?...

I have PDE i trying to solve the equation using series.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = Pi, series, order = 2);

Give me: "Error, (in DifferentialAlgebra:-RosenfeldGroebner) unexpected occurrence of the non-rational constants {Pi} in the given input" ?

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) =gamma, series, order = 2);#gamma = 0.5772156649,Gives ERROR ?

If I  change instead of Pi is e or exp(1) works fine.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = exp(1), series, order = 2);#OK.

It's a bug, design or  something else ?

## Error, (in dsolve/numeric/process_input) system mu...

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

## do not show answer ...

solve does not show result!!

dtm.mw

fsolve.mw

## Extra text behind Code Edit Region...

Dear friends,

maybe, somebody knows how to remove annoying text of the first line of a Code Edit Region when a Region is collapsed.

Here, Region in expanded state:

But after collapsing the first line still remains:

## about maple kernel connection not available...

when I  have transformed symbol expression  from matlab 2017b to  maple 2018 , maple took a mistake that  "maple kernel connection not available", What  is the  reason？Can anyone help me？Thank you！

## Why the difference?...

How to explain the difference in the outputs of

```restart; ans1 := solve(eval({-4*a^2+x^2+y^2 <= 8*y-10*x+4*a-40, -a^2+x^2+y^2 <= 6*x-4*y-13}, a = -9), {x, y});
ns1 := {x = 3-sqrt(-y^2-4*y+77), -11 <= y, y < 13/25},
{-11 < y, x < -5+sqrt(-y^2+8*y+273), y < 13/25, 3-sqrt(-y^2-4*y+77) < x},
{x = -5+sqrt(-y^2+8*y+273), -11 < y, y < 13/25}, {y = 13/25, -141/25 <= x, x <= 291/25},
{x = 3-sqrt(-y^2-4*y+77), y <= 7, 13/25 < y},
{13/25 < y, x < 3+sqrt(-y^2-4*y+77), y < 7, 3-sqrt(-y^2-4*y+77) < x},
{x = 3+sqrt(-y^2-4*y+77), 13/25 < y, y < 7}```

and

```restart; ans2 := solve(eval({-4*a^2+x^2+y^2 <= 8*y-10*x+4*a-40, -a^2+x^2+y^2 <= 6*x-4*y-13}, a = -9), [x, y]);
ans2 := [[x < 3, -6 <= x, y = -2-sqrt(-x^2+6*x+72)],
[x < 3, -6 < x, y < -2+sqrt(-x^2+6*x+72), -2-sqrt(-x^2+6*x+72) < y],
[x < 3, -6 < x, y = -2+sqrt(-x^2+6*x+72)], [x = 3, y <= 7, -11 <= y],
[x <= 291/25, 3 < x, y = 4-sqrt(-x^2-10*x+264)],
[x < 291/25, 3 < x, y < -2+sqrt(-x^2+6*x+72), 4-sqrt(-x^2-10*x+264) < y],
[x < 291/25, 3 < x, y = -2+sqrt(-x^2+6*x+72)]]```

?

In the former x is expressed through y and in the latter y is expressed through x. I find explanation  in neither ?solve nor ?solve,details.

## unable to plot LegendreQ...

I do not know what I am doing wrong. I am trying to plot each of the solutions to an ODE. One of the solutions Maple gives is  LegendreQ((1/2)*sqrt(5)-1/2, x) and the other is LegendreP((1/2)*sqrt(5)-1/2, x)

Maple can plot the  LegendreP, but gives an error plotting LegendreQ((1/2)*sqrt(5)-1/2, x)

```ode:=(1-x^2)*diff(y(x),x\$2)-2*x*diff(y(x),x)+y(x)=0:
sol:=dsolve(ode,y(x));
```

sol := y(x) = _C1*LegendreP((1/2)*sqrt(5)-1/2, x)+_C2*LegendreQ((1/2)*sqrt(5)-1/2, x)

Now when I do

`plot(LegendreQ((1/2)*sqrt(5)-1/2, x),x=-1..1);`

Maple says

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

Why is that? I tried x=-0.5..1 and x=0.5..1 and keep getting same error message. It works ok for

`plot(LegendreP((1/2)*sqrt(5)-1/2, x),x=-1..1);`

Mathematica can plot both with no problem.

## Calculate integral?...

int(exp(-sec(t))*cos(t)/(-1/4+sin(t)^2), t = 0 .. (1/2)*Pi, CauchyPrincipalValue = true, numeric = true);

Returns unevaluated for me.

```I tried all the methods in HELP documentation and I failed.
Integral is singular at point 1/4.

```

Thank you.

## How to find suitable initial condition...

Hello my friends

I have a problem with initial condition for below system of differential equation

sys := {6*(diff(a(t), t))^2+12*a(t)*(diff(a(t), t\$2))-3*a(t)^2*phi(t)^(-2*c)*sqrt(1-alpha*(diff(phi(t), t))^2), 2*c*a(t)^3*phi(t)^(-2*c-1)*sqrt(1-alpha*(diff(phi(t), t))^2)-3*alpha*a(t)^2*phi(t)^(-2*c)*(diff(a(t), t))*(diff(phi(t), t))/sqrt(1-alpha*(diff(phi(t), t))^2)-alpha*a(t)^3*phi(t)^(-2*c)*(diff(phi(t), t\$2))/sqrt(1-alpha*(diff(phi(t), t))^2)+2*c*alpha*a(t)^3*phi(t)^(-2*c-1)*(diff(phi(t), t))^2/sqrt(1-alpha*(diff(phi(t), t))^2)-alpha^2*a(t)^3*phi(t)^(-2*c)*(diff(phi(t), t))^2*(diff(phi(t), t\$2))/(1-alpha*(diff(phi(t), t))^2)^(3/2), R(t) = 6*((diff(a(t), t))^2/a(t)^2+(diff(a(t), t\$2))/a(t)), W(t) = -phi(t)^(-2*c)*sqrt(1-alpha*(diff(phi(t), t))^2)/(1/a(t)^3+a(t)^3+phi(t)^(-2*c)/sqrt(1-alpha*(diff(phi(t), t))^2))}

I set {c,alpha}={1,1} but initial conditon is problem ... since I got the following message from maple to illustrate diagrams of W(t), a(t) and even phi(t)

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

with the best regard

## Controlling plot range in a parametric 3D plot...

Hi,

I would like to control the extents of my 3D parametric plot. Increasing the grid creates too many gridlines and I just get a black plot  (and I still don't get the extent in the y-coordinate that I want).

Any suggestions how I might be able to get this plot from -360 to 0 and -20 to 60 completely filled in? (see attached workbook).

Any suggestions on how to control the gridlines?

An idea of what I am trying to do...I want to plot argument(z/(1+z)) vs. argument(z)*180/pi vs. 20*log10(abs(z)) with contours of argument(z/(1+z)) and 20*log10(abs(z/(1+z))
This is a 3D plot of the output phase of a Nichol's Chart (with the output contours of the Nichol's chart).

Thanks.

phaseplot.mw

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