John2020

175 Reputation

5 Badges

2 years, 38 days

MaplePrimes Activity


These are replies submitted by John2020

@tomleslie 

Yes, you and dear carol are right.

I realized my mistake a couple of hours ago.

sorry!

@Carl Love 

Dear friend,

Thanks a lot for consideration.

But, x[0](tau) and y[0](tau) are independent from each other. For this reason, I have this expectation that maple understand this and use separation method and then splits the eq to 2 equations as:

eq[1]:=diff(x[0](tau), tau) + x[0](tau)=0;

eq[2]:=- diff(y[0](tau), tau) - y[0](tau)=0;

then the solutions with that boundary conditions are exactly exp(-tau) as I mentioned.

Is there any way to get this?

@acer 

Dear friend,

Thank you very very much.

It is exactly what I wanted.

@acer 

Hi,

one (or 2 or 3) real non-zero (if possible) root(s) for each variable (a[1],a[2],...) is sufficent. 

@Carl Love 

Dear friend,

Thank you very very much.

@Axel Vogt  

Dear friend,
Thank you very much for your help.
But what I want is another thing which I wrote in reply to @Carl Love .

@Carl Love 

Dear friend,
Thank you very much for your help.
But what I want is for example to write SBesselJ(0,x) instead of sin(x)/x and etc.
Indeed I want to translate sin and cos functions to spherical Bessels.
Like this picture:

 

@acer 

Dear friend,

Yes, Exactly!!

I was looking for such codes.

It works very well.

Thank you very very much.

@acer 

Dear friend,

Thank you very much.

Is there a way to get 2*k ?

@vv 

Dear firend,

Thanks a lot, but it is not correct:

First of all, I want "m" not "p", and as you see the answer must be m=4*cos(varphi(t)).

Your code does not work, see, I replaced p by m and recieved erro:

restart;

with(Physics):

r := x*(diff(theta(t), t))^2+y*(diff(varphi(t), t))^2+z*(diff(theta(t), t$2))+w*diff(varphi(t), t$2)+p*m;
g := (4*(f+T))*(diff(theta(t), t))^2+u*(diff(varphi(t), t))^2+(f+9)*(diff(theta(t), t$2))+4*s*diff(varphi(t), t$2)+p*4*cos(varphi(t));

eval(r-g, [theta=(t->1+t+t^3), varphi=(t->1+t+t^7)]): # or similar
[coeffs(convert(series(%, t), polynom), t)]:
solve(%, [x,y,z,w,m]):
solve(%[1], [x,y,z,w,m]);

 

Error, invalid subscript selector
Error, invalid subscript selector

 

@vv 

Thanks a lot for your reply. It is also very good and applicable, thank you very much, But

It does not work for the following example like other approaches:

restart;

with(Physics):

r := x*(diff(theta(t), t))^2+y*(diff(varphi(t), t))^2+z*(diff(theta(t), t$2))+w*diff(varphi(t), t$2)+p*m;
g := (4*(f+T))*(diff(theta(t), t))^2+u*(diff(varphi(t), t))^2+(f+9)*(diff(theta(t), t$2))+4*s*diff(varphi(t), t$2)+p*4*cos(varphi(t));
eval(r-g, [theta=(t->t^3), varphi=(t->t^7)]): # or similar
solve([coeffs(%, t)], [x,y,z,w,m]);
simplify(eval(r-g, %[1]));   #check

 

Do you have an idea to solve it?

@ecterrab 

Thanks a lot for your reply. It is really simple and short, thank you very much, But

It works only in the cases that all its terms have diff:

For example, in the following case it not works, however, other approaches are like this one, fail:

restart;

with(Physics):

r := x*(diff(theta(t), t))^2+y*(diff(varphi(t), t))^2+z*(diff(theta(t), t$2))+w*diff(varphi(t), t$2)+p*m;
g := (4*(f+T))*(diff(theta(t), t))^2+u*(diff(varphi(t), t))^2+(f+9)*(diff(theta(t), t$2))+4*s*diff(varphi(t), t$2)+p*4*cos(varphi(t));
PDEtools:-Solve(r = g, {w, x, y, z,m}, independentof = t)

 

Do you have an idea to solve it?

@acer 

Hello,

A complicated example that the codes not work for it is as follows:

restart;

with(Physics):

r := x*(diff(theta(t), t))^2+y*(diff(varphi(t), t))^2+z*(diff(theta(t), t$2))+w*diff(varphi(t), t$2);
g := (4*(f+T))*(diff(theta(t), t))^2+u*(diff(varphi(t), t))^2+(f+9)*(diff(theta(t), t$2))+4*s*diff(varphi(t), t$2);

solve(identity(subsindets(r=g,specfunc(:-diff),freeze),
               freeze(:-diff(theta(t),t))),
      [x,y,z,w]);
frontend(solve,[identity(r=g,diff(theta(t),t)),[x,y,z,w]],[{`+`,`*`,`=`,list,specfunc({identity})},{}]);

 

Could you please help me to extend the previous codes for this problem?

@acer 

WoW! Fantastic!

Thanks a lot for your great help.

I really do not how I can appreciate you.

You helped me so much.

Thank you very very very very .... very much.

I wish all the best to you and your family.

Sincerely yours,

J.

@acer 

This new way also works fine!

Thanks a lot.

Thank you very very much, dear friend.

Thanks for spending time. Thank you so much.

1 2 3 Page 1 of 3