nm

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These are questions asked by nm

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.

These are some basic questions on using packages from Maple Cloud. I only used it once or twice so far.

When I click on the "cloud" icon, on top right corner of the menu, I see on the left panel "Math apps" then below it "packages" and then below it is says "installed".

When I click on "installed", I see one package that I installed sometime ago.

1) How does one uninstall a package listed in the "installed" list? I see no option to do this.

2) How does one know if the "installed" package needs to be updated or not? And if so, how does one updated it? 

3) In the "packages" list, I see "physics Updates".  Now,  I did install this earlier (1-2 weeks ago). Then why is it not listed also under the "installed" list? And how does one know if they have installed a package that shows in the "packages" list?

There is no marker or anything there to tell one they have installed it or not.  Is one supposed to go look in the "installed" list to manually check if they installed it or not?

4)What happens if one install a package/app they have installed before. Will the new package overwrite the older version automatically?

5) It seems packages installed go to some temporary folder. Is there a way to configure it, so that all packages installed go to some other user defined folder. This way, if one moves to a new PC or such, they do not lose all the packages they have installed? 

It seems these basic functionalities are missing: 1. option to uninstall a package. 2. Marker of some kind to tell one if they installed something listed in the "packages" list. 3. Marker to tell one if a package they have installed needs to be updated if there is a newer version on the cloud.

Only options I see are: Install, view, share link and search. That is all. All the above also applies to "Math apps".

Using Maple 2018 on windows.

Why is assume(...) do_something();  gives an error when I run the code one more time, but do_something() assuming ...; do not give an error when everything else is the same?

Is there semantic difference between the two forms? I thought they should work the same way. Here is an example

#in separate cell
restart;

#in separate cell
interface(showassumed=0):
pde := diff(u(x, t), t)=k*diff(u(x, t), x$2):
ic:=u(x,0)=0: bc:=u(0,t)=t:
assume(x>0);assume(t>0);assume(k>0):
sol:= pdsolve({pde,ic,bc},u(x,t)):

#in separate cell. Now this gives error
interface(showassumed=0):
pde := diff(u(x, t), t)=k*diff(u(x, t), x$2):
ic:=u(x,0)=0: bc:=u(0,t)=t:
assume(x>0);assume(t>0);assume(k>0):
sol:= pdsolve({pde,ic,bc},u(x,t)):
#error message now

Here is screen shot

Now will do the same, but use assuming. Now there is no error

#in one cell
restart;

#in one cell
interface(showassumed=0):
pde := diff(u(x, t), t)=k*diff(u(x, t), x$2):
ic:=u(x,0)=0: bc:=u(0,t)=t:
sol:= pdsolve({pde,ic,bc},u(x,t)) assuming x>0,t>0,k>0:

#in one cell, no error
interface(showassumed=0):
pde := diff(u(x, t), t)=k*diff(u(x, t), x$2):
ic:=u(x,0)=0: bc:=u(0,t)=t:
sol:= pdsolve({pde,ic,bc},u(x,t)) assuming x>0,t>0,k>0:

Here is screen shot

Why does one give an error, but the second one does not?

I thought they work the same way. Which method is recommended to use?

assume(...); do_something(); 

or 

do_something() assuming ...;

Maple 2018 on windows.

Could some Maple expert help me understand why pdsolve gives me this error message from trying to solve this Schrödinger pde and if there is a work around?

restart;
pde:=I*diff(f(x,t),t)=-diff(f(x,t),x$2)+2*x^2*f(x,t);
bc:=f(-infinity,t)=0,f(infinity,t)=0;
sol:=pdsolve([pde,bc],f(x,t));

I must be doing something wrong, but do not see it.

Mathematica solves the above as follows

pde=I D[f[x,t],t]==-D[f[x,t],{x,2}] + 2 x^2 f[x,t];
bc={f[-Infinity,t]==0,f[Infinity,t]==0};
sol=DSolve[{pde,bc},f[x,t],{x,t}]

thank you

Does any one know of a trick to make Maple solve this PDE using pdsolve?

restart;
pde:=diff(u(x,t),t)+diff(u(x,t),x)=0;
bc:=u(0,t)=0;
ic:=u(x,0)=x;
sol:=pdsolve({pde,ic,bc},u(x,t));

I have tried all HINTS and assumptions and Maple just returns () as solution.

Mathematica solve this as follows

ClearAll[u,x,t];
pde=D[u[x,t],t]+D[u[x,t],x]==0;
bc=u[0,t]==0;
ic=u[x,0]==x;
sol=DSolve[{pde,ic,bc},u[x,t],{x,t}]

 

Heavidside theta is basically a unit step function.

 

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