Any one know if it possible to see the steps used by the limit() function as one does with many other functions such as dsolve and int ?  This is what I tried

restart;
infolevel[limit]:=5;
interface(verboseproc=3);
limit(x^2 *log(x),x=0);

But I see no steps, only the final answer. Are not all Maple functions possible to trace? How does one know which functions can generate trace and which do not?

I am using Maple 2016.1

I wanted to see something like:

let x=1/t, hence expression becomes  (-ln t)/t^2, now taking limit as t->infinity. Applying L'Hopital rule, limit t->infinity of -1/(2 t^2) which gives zero.

I assumed this is something what Maple does internally, (but there are other ways also) and wanted to see what Maple does.

I have never seen DEtools:-odeadvisor hang before. I've seen dsolve itself hang many times, but not odeadvisor. Is this a bug? Maple 2016.1 on windows.

restart;
eq:=(2*y(x)*diff(diff(y(x),x),x)-diff(y(x),x)^2)^3+32*diff(diff(y(x),x),x)*(x*diff(diff(y(x),x),x)-diff(y(x),x))^3 = 0;
DEtools:-odeadvisor(eq);

Now it hangs. Waited for more than one hr. This is an ODE from a book. Do others see the hang as well?

The ODE diff(y(x),x) = sec(x)^2*sec(y(x))^3  can be solved as separable. So the answer should be 

simple_answer:=sin(y(x))*(cos(y(x))^2+2)=C_1+3*tan(x);

as can be seen by direct integration of each side of the differential equation. I am trying to make Maple give the same answer, but not having any luck. 

restart;
ode:=diff(y(x),x) = sec(x)^2*sec(y(x))^3;
sol:=dsolve(ode, y(x),implicit);

I tried simplify(sol,trig) and tried simplify(sol,size).  Both Maple answer, and the simple answer solve the ODE.

Is there a way to make Maple dsolve give the simpler answer, or simplify/convert the answer it gives to the simpler one? I am newbie in Maple.

Hello; I found another ODE which Maple gives division by zero on.  Is this also a bug? 

dsolve(x*(a^2*x+(x^2-y(x)^2)*y(x))*diff(y(x),x)^2-(2*a^2*x*y(x)-(x^2-y(x)^2)^2)*diff(y(x),x)+a^2*y(x)^2-x*y(x)*(x^2-y(x)^2) = 0, y(x));

Error, (in dsolve) numeric exception: division by zero

This is from a book. Using Maple 2016.1 on windows.

Maple 2016.1 on windows. This ODE from a book, and Maple gives division by zero. Is this a bug or expected?

ode:=(a^2*x+(x^2-y(x)^2)*y(x))*diff(y(x),x)+x*(x^2-y(x)^2) = a^2*y(x);
dsolve(ode, y(x));

Error, (in dsolve) numeric exception: division by zero

Mathematica gives this to same ODE, but no division by zero.

DSolve[x*(x^2 - y[x]^2) + (a^2*x + y[x]*(x^2 - y[x]^2))*y'[x] == a^2*y[x], y[x], x]

Solve[x^2/2 - (1/2)*a^2*Log[x - y[x]] + (1/2)*a^2*Log[x + y[x]] +y[x]^2/2 == C[1], y[x]]

Where is the division by zero coming from in Maple?

2016.1 on windows.