@torabi The command is what you used and what I used in the form
invlaplace(rhs(sol3),s,t);

It was not successful, however. invlaplace couldn't do the inversion, but just used linearity to get

Why is the title "Shooting Method" ?
There is no shooting going on. `dsolve/numeric/bvp`doesn't use a shooting method.

@Bendesarts Using your condition1 I tried

indets(condition1,`^` );

There are no squared sine functions among the members of the output:

@Christopher2222 With few exceptions (e.g. Edgardo S. Cheb-Terrab and Robert J. Lopez), Maple employees rarely participate on MaplePrimes, but leave the discussion to the members.
I'm sure there are very good reasons for that, among those

(1) too busy working on matters directly related to Maple software;
(2) allowing a free discussion among members without interfering with an "authoritative" or "official" verdict on the issue.

Both of those two are perfectly legitimate and honorable reasons.

But the spam issue is different as it has nothing to do with the behavior of Maple software, so some reaction from the responsible part would be appreciated.

@9009134 Why not keep the RootOf. Notice that it is indexed with 1,2,and 3.
Try e.g. setting all parameters to 1:

nms:=indets(A,name);
eval([Sol],nms=~1);
allvalues(%);
evalf(%); #If you want floats you can skip the previous step.

I didn't even think of trying to integrate u1 symbolically before, but doing that improves the result.
For convenience I bring all of the code.
I have made two extra changes. In series I have used the order 5 instead of 3.
Also it seems to help to use the procedural form for input to evalf/Int:

restart;
Digits:=15:
tD := 20;
u:=4/Pi^2*( 1 - exp(-x^2*tD) ) / ( x^3*( BesselJ(0,x)^2 + BesselY(0,x)^2 ) );
series(u,x,5); #Replaced 3 by 5
u1:=convert(%,polynom);
U1:=int(u1,x=0..1/2);
#evalf(Int(u-u1,x=0..1/2,epsilon=1e-6));
evalf(Int(unapply(u-u1,x), 0..1/2, epsilon=1e-12));
evalf(U1);
res1:=%%+%;
res2:=evalf(Int(u,x=1/2..infinity));
res1+res2;
simplify(%); # Result12.3201290912317

@Carl Love Yes, I would bulk delete.

The problem now is that the time it takes to delete N items is proportional to N.

Way most of the spam can be seen as such just from the title, but a bulk delete function could show the contents of the selected items so a quick eye scan can eliminate any doubt before deletion.
Real obvious items having titles like the one I'm staring at to the right of me http://testoteronebooster...etc...etc could as you suggest be deleted automatically.

Today Sept. 20 at 1 p.m. (Central European Summer Time) I counted 31 spam posts after clicking Recent Posts.

No way I'm going to start deleting those. I give up.

@Christopher2222 I sometimes wonder why somebody is filling this site with this cr.p, which nobody here can be expected to be interested in.
Is it simply because it is so easy to do and costs nothing (or close to nothing) and that maybe one in a thousand will bite?

I think this site relies on the users to remove the spam. That is OK as long as there is little. But that is not (or no more) the case.
The introduction of the feature "Delete as Spam" hasn't been helping anything it seems.

I delete quite a lot, but get tired of it besides irritated. You have to delete one at a time, which may seem reasonable, but the process is a two step procedure, so deleting 10-20 posts ("questions") is boring at best.
Could some of us delete several at a time then it might be tolerable.

Actually I suggested deleting anything that contains http in the title some time ago.

It would be nice if one didn't have to wake up to 10-20 spam "questons" or posts about weight loss or penis extensions or whatever. Why doesn't MaplePrimes have a spam filter?
It is irritating to have to delete that much spam or more before you can see anything of value.

@max125 You can report a bug (an SCR) in MaplePrimes:
Go to the top left to More. Choose Submit Software Change Request.

@nm Yes, and p is not declared local.

membertype assigns to p.

The sequence of locals:

eval(op(2,eval(Logic:-Satisfy));

       B, vars, foundvars, extravars, i, result, s, u, T, V

@tomleslie Change maxstep=0.1 to stepsize=0.1 in DEplot3d then the result will look like the one you get from odeplot if you use:

sols:=dsolve( desys, numeric, maxfun=0,stiff=true,range=0..1000);
plots:-odeplot(sols,[B[1](t), B[2](t), C(t)], 0..1000,refine=1);

@Carl Love The image in the question is an image of 2-D math input, which I never use. But if I in a worksheet on a new input line write
pi;

Then select it with the mouse, right click and choose Convert to 2-D Math Input then press Enter and finally evalf(%);

then I get 3.141592654.
Yes, just another reason not to use 2-D math input.

# The text version uses commas instead of periods, so was obviously not used by the questioner (Niek).