@Marcel123  I work in the classic interface  Maple 2015.1, in which no such messages. The problem is that  D - is a protected name. As a workaround use the other names, for example

restart;

sol := dsolve({diff(x(t), t, t)-(diff(x(t), t)) = 1+t^2+x(t)^(3/2), diff(x(t), t, t) = y(t), x(0) = 0, y(0) = 1, (D(x))(0) = 0}, numeric);

sol(0.5);

x := t->rhs(sol(t)[2]):

Dx := t->rhs(sol(t)[3]):

D2x :=t->rhs(sol(t)[4]):

x(0.5),  Dx(0.5),  D2x(0.5);

@Markiyan Hirnyk  As I wrote in my answer, this is very simple, so I did not touch this issue.

@Carl Love  for your diligent and detailed analysis of all over this situation.

@tomleslie  In my Firefox, I was able to read that Carl wrote about:

@Carl Love  for the detailed explanation.

@Carl Love  Vote up.  Two questions:

1) What is the significance  R:= Vector() .  Why can not we just take the indexed variable  R ?

2) What is  _rest ?

The next version works  like your one:

SplitScan:= proc(f, L::list)

local R, k:= 0, j, last:= 1;

     for j from 2 to nops(L) do

          if f(L[j-1], L[j]) then

               k:= k+1;

               R(k):= L[last..j-1];

               last:= j

          end if

     end do;

     [seq(R(i), i= 1..k), L[last..]]

end proc:

@Markiyan Hirnyk  I know it. This is a feature of the solution.

For example (equation for  tan(x) ) we get the same warning:

sol:=dsolve({diff(y(x),x)=1/cos(x)^2, y(0)=0}, numeric);

plots[odeplot](sol, [x, y(x)], x = 0 .. 2, view=[0..2,0..10]);

@Carl Love  convenient for a large number of plots.

plot([seq(`[]`~(x,y||i), i=1..2)]);

@Rouben Rostamian   Here is a shorter version of the same plotting without  plots  package:

x := [0., .20, .40, .60, .80, 1.0]:
y1 := [0., .20, .40, .60, .80, 1.0]:
y2 := [0., .64, .96, .96, .64, 0.]:

plot([`[]`~(x,y1),`[]`~(x,y2)]);

I think I misunderstood the meaning of the original question in my answer.

See the same question

@toandhsp 

restart:

k:=combine((sin(x+Pi/3))^2);

sol:=solve(k=1/4, x, AllSolutions = true, explicit);

sol1, sol2:=subs({_B1=0,_Z1=n},sol), subs({_B1=1,_Z1=n},sol);

@Carl Love  Unfortunately I have the right to put only 1 vote up.

@Carl Love  for a very useful remark. I fixed this defect in code.

Please provide explicitly your system  V . Probably needed extra options in  solve  command.

@Carl Love  Of course, in the original example, there is no problem, because determinant of the system at any  b  is not equal to 0, and it has a unique solution for any b. In other cases (if first we use solve) there may be a wrong solution.

Example:

restart;

solve({b*x+y=1, x+b*y=1}, {x,y});

eval(%, b=1);

The solution is erroneous because for b = 1, there are infinitely many solutions.

The correct solution

solve(eval({b*x+y=1,x+b*y=1}, b=1), {x,y});

                   {x = 1-y, y = y}

Another example:

eval(solve(sqrt(x+b)>x, x), b=1);

Warning, solutions may have been lost

The correct solution:

solve(eval(sqrt(x+b)>x, b=1), x);

               RealRange(-1,Open(1/2*5^(1/2)+1/2))

Thus, variant  solve(eval...)  is more reliable than  eval(solve...)