In fact, the found solution  sol  is true not only for positive, but also for all real values x . To acer's two methods, I added plotting. Of course this is not mathematically rigorous, but still convincing enough:

restart;
ode:=diff(y(x),x)-y(x) = x*y(x)^(1/2):
ic:=y(0)=4:
sol:=dsolve([ode, ic],y(x));
check:=odetest(sol,ode);
simplify(eval(check,x=2*t)) assuming real; # The first way
simplify(simplify(check, {exp(x)=exp(x/2)^2})) assuming real;  # The second way
plot(check, x=-10..10, -1e-6..1e-6, axes=box, size=[1000,300]);  # The third way

You cannot place the contents of your file here, but you can place a link to the file here using the bold green arrow in the MaplePrimes editor. Then everyone who has Maple will be able to upload your file to themselves and understand what the problem is.

@ruhamdam  I don't see an error:

restart;
L:=proc(P,v)
if P=x then  x*y elif 
P=y then  1 elif
P=z then  z^2 elif
nops(P)=1 and not (P in v) then  0 elif
type(P,`+`) then  map(L,P,v) elif
type(P,`*`) or type(P,`^`) then if type(P,`^`) then  op(2,P)*op(1,P)^(op(2,P)-1)*L(op(1,P),v)  else  `+`(seq(`*`(({op(P)} minus {p})[])*`if`(p::numeric,0,`if`(p in v,L(p,v),op(2,p)*op(1,p)^(op(2,p)-1)*L(op(1,p),v))),p={op(P)})) fi; fi;
end proc:

L(3+x,[x,y,z]);
L(3,[x,y,z]);

ABCD  is a square and 2 angles  ECF  and  BCG  are known  (in degrees). Find angle  GFA  (see a pic. below). 

It is easy to check that this angle is the original trigonometric expression. I know a very simple geometric solution (without Maple and without any trigonometry), but I will not show it for now, so that everyone can enjoy their own solution.

@acer  We have to do this to get a solution, since Maple 2018 returns NULL for

solve(csgn(ln(x+1)-2)=-1) assuming real;

@acer  Should be  x+1>0  (in real domain)

@acer  Yes, I noticed your answer was updated after my comment was posted.

@acer  Thank you. In my Maple 2018.2  I get

simplify(convert(Expr,exp));

For grouping expressions in Maple, only parentheses (not square brackets) are used. Square brackets are used when creating lists. Also I didn't understand what  `–`(0.3364722366, 1.2)  means.
So correct your expression first.

@nm  Thank you. Yes, Mathematica's capabilities are impressive.

@nm  Please execute in Mathematica the code  Simplify[ f ]  or  FullSimplify[ f ] . Can it to simplify the expression  f  to the expression  g  without knowing  g ?

@Earl   Just replace  y  with  y(x)  and use the  d  procedure. All terms of the resulting equation have  dx  as a factor. We can reduce it, or we can do nothing - this does not affect the result:

restart;
d:=z->diff(z,x)*dx:
DE:=y(x)*cos(x)*d(y(x))-sin(x)*dx;

dsolve(DE);
plot([seq(eval(y(x),%[1]),_C1=-3..3),seq(eval(y(x),%[2]),_C1=-3..3)], x=-Pi/2..Pi/2, scaling=constrained, size=[500,500], view=[-Pi/2..Pi/2,-2..2]);

@Carl Love I understand very well that my procedure can be improved both in terms of its effectiveness and length. But there are also pedagogical considerations. You can see for yourself that OP is a complete newbie to coding. My goal was to make minimal changes to the code to make it work and at the same time maintain the overall intent of the person who wrote the code. It is great that you are always looking for the best solutions. At the same time, I think it is not entirely ethical to speak out here about the vote.

@maxprog I beg your pardon. I do not have a maple calculator.

What does  2 z y =  mean?