@JohnS 

sorry, not following you, so not able to know what to do, But I am sure someone who knows this better than me will be able to help. good luck.

@Carl Love 

Great. thanks. So may be this is a skill that needs to be acquired to know which command to use and which not to use each time, and it is not something one can reason about using logical steps.

For example, why would

convert(s,trig);
combine(%):

work, but not

convert(s,trig);
simplify(%);

and not

convert(s,trig);
convert(%,sinh);

and not

convert(s,trig);
convert(%,trigh);

and why simplify was needed to tell Maple that is same as

I mean, if this processes is based on trial and error method, then that is not a good way to go about it, but if there is a logic behind it, then that will be better.

computing the indefinite integral, then evaluating it on the intervals, then letting {p=1,n=1,q=1,m=1} in the result gives a divide by zero. Not -(1/2 I)/Pi. Just an observation, that is all.

restart;
assume(m::integer, n::integer, p::integer, q::integer,x::real):
h:=(x,m,n,p,q)->-(1/8*I)*(exp((2*I)*Pi*x)-1)^2*(exp(-(2*I)*Pi*x*(n-q+2))-exp(-(2*I)*Pi*x*(n-q+1)))/(Pi^3*x*(m-x)*(p-x)):
sol:=int(h(x, m, n, p, q), x):
sol:=subs(x=infinity,sol)-subs(x=-infinity,sol):
subs({p=1,n=1,q=1,m=1},sol);

     Error, numeric exception: division by zero

@acer 

strange that the good and bad ODE both give same analytic solution.

@Carl Love 

thanks. That is actually what I tried. it puts the 1/2 below the whole expression, which is not what I want. I wanted it to show like you showed it. I am using Maple 17.02 on windows 7, 64 bit. I use worksheet. Here it is:

@Carl Love 

Actually, I just tried it and it worked. No special reason. But simplify() works at that stage, so will edit my answer and replace convert to simplify.

I assumed you had a type  in (x+y)^2+(1)/x+y  and you meant  (x+y)^2+  1/(x+y), else the result you want to obtain do not follow....you might want to fix your question

@Carl Love 

Maple prime will not let me edit my own answer, it says "You do not have permission to delete this document". So, I'll see if it works here:

plot([f(x),diff(f(x),x)],x=-3..3,discont=true,legend=[typeset("f(x)"),typeset("f'(x)")]);

eq:=(3*x-y(x))*diff(y(x),x)=2*x;
dsolve(eq,y(x));

@Alejandro Jakubi 

"So, I prefer going through the menu"

Sure, and that is what I did. But this option is not in the menu. That was my point. I was looking for something like setup... or options.... in the menu, but did not see it. I am using 17.02, so may be your version has this in the menu. But now I'll remember to check all those icons from now on ;)

@Alejandro Jakubi 

That was easy, thanks. I did actually look at the help menu there, but saw nothing but overlooked to check what those icons up there for. Now I see that one icon does the trick. (needed to put the mouse over it for a second to see the pop-up help and see what it means).

You can see easily that the is that assumptions are not used. that is all. Replace `assuming x>0` with `assuming x>1000` and you'll get the same answer.

@ANANDMUNAGALA 

Hello;

The command is simply Determinant(). This is a maple command. If the result is not zero then L.I.

I do not understand what is the issue.

@ANANDMUNAGALA 

Hello;

The command is simply Determinant(). This is a maple command. If the result is not zero then L.I.

I do not understand what is the issue.

@Carl Love 

Yes, ofcourse it can give a solution for arbitrary u, and that what the code I have did?

What I meant is that one needs an actual definition of u(t) to do something with the solution, in terms of plotting it, evaluating it, etc...

May be I should take my engineering hat off when I am in this forum :)