John2020

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2 years, 86 days

MaplePrimes Activity


These are replies submitted by John2020

@dharr 

Dear friend,

Thank you very much.

@Rouben Rostamian  

Dear friend,

Thanks a lot for your comments and helps.

I'll consider the problem again.

@dharr 

Dear friend,

Thanks a lot for your help.

Two conditions correspond to the first and third time intervals.

I want that maple to distinguish this and solve the ode at the first interval with the first bc and solve the ode at the third interval with the second bc and give me the true result, but ....

@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?

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