Download maple_sol.mw

screen shot

Humm. Did you not ask this same thing in https://www.mapleprimes.com/questions/243707-Recalcitrant-Differential-Equation

and got a reply for it?

D(f@g)   works because f and g these are not defined, so maple can't take their derivatives.

But ln and cosh are known functions to maple so it can take their derivative . So it is evaluation issue.

To do what you want you can try freezing them

Download test3.mw

Replace y(x) by y and add assuming x>positive. 

opps, thanks to all comments below, fixed more.

Changed to only assuming x>0 since IC at negative y

Download test3.mw

L:=[1/2, 1/3, 1/4];
`%+`(op(L))=`+`(op(L))

Maple can't find general solution for this ode, but it can find particular soltutions

ode:=(1+y(x))*diff(y(x),x$2)=1+x;
yp:=DEtools:-particularsol(ode,y(x));

map(X->odetest(X,ode),[yp])

[0,0]

plot(rhs~([yp]),x=-3..3)

How can the length of the result series be controlled? 

You can use the order=N option

sol:=dsolve([ode,IC],y(x),'series','order'=5);
sol:=dsolve([ode,IC],y(x),'series','order'=10);

A:=sqrt(2)/( sqrt(1-b^2)*sqrt(2+(-x-1)*b^2) );
subsindets(A,'`^`(anything, -1/2)', f -> 1/sqrt(simplify(op(1,f))));

The above simplifies sqrt(*) in denominators.   If you want to simplify sqrt(*) in numerator, change it to 

subsindets(A,'`^`(anything, 1/2)', f -> sqrt(simplify(op(1,f))));

And if you to do both on expression, simply do the above twice, one for the numerator and next for the denominator.

restart;

max_X:=8: max_Y:=5:

grid_points:= [seq(seq([n,m],n=0..max_X),m=0..max_Y)]:
H_lines := [ seq([ [0,y],[max_X, y] ], y = 0..max_Y) ]:
V_lines := [ seq([ [x, 0],[x, max_Y]], x = 0..max_X)]:
the_points := plots:-pointplot(grid_points, symbol=solidcircle, symbolsize=12, color=red):
p_lines  := plot([op(H_lines), op(V_lines)], color=blue, thickness=2):

plots:-display(the_points, p_lines, title="my grid", view=[0..max_X, 0..max_Y]);

You missed up your `t` in the loop.

Simplify add t:='t'; after the loop to clear it.

cpu_time:=time()-begin;
plots:-pointplot3d([seq(pt[j],j=0..n)],axes=normal,symbol=cross,symbolsize=8,color=red,labels=["t","x","y"],orientation=[-90,0]);
t:='t'; # MAKE SURE TO DO THIS
sys:=diff(X(t),t)=Y(t),diff(Y(t),t)=F(X(t),Y(t));
vars:={X(t),Y(t)}: 
ic:=X(0)=0.2,Y(0)=0.1:

Download A.mw

one way is

eq:=x^4-12*x-12=0;
solve(eq,x,'explicit');

Another way

sol:=solve(eq,x):
allvalues([sol]);

And if you want numerical values (easier to read) just use evalf as in

sol:=solve(eq,x):
allvalues([sol]);
evalf(%);

Notice the complex roots are conjugate of each others as would be expected.

change   DU(.99999) = -.3401375821   to   D(U)(.99999) = -.3401375821

good  catch. You've found internal Maple bug. The bug is in simplify not convert.

A:=convert(WhittakerW(7/3,1,hypergeom([1],[2],z)),trig);

And now

try: 
    simplify(A);
catch: 
end try;

Error, (in expand/sin) too many levels of recursion

These internal Maple bugs can not be cought using try/catch by design. 

I'll report it for Maplesoft now so they could try to fix it before 2026 is supposed to be released next month.

eq := ((Cn - a)^2 + (P - d - b)*x^2 + Cn - a - b)/y(Cn - a)^2
simplify(eq,{Cn - a =X , P - d - b =S})

replace your last call

plot(g(x), x = 1 .. 50);

with this

plot('g(x)', x = 1 .. 50);

This delays evaluation of g(x) until x has numerical value.

for first one, for getting list of package you could do  ?index,package;

You will get this

in the worksheet.