@Preben Alsholm 

Many thanks for the nice work; that will keep me motivated in learning some Maple now...

@Preben Alsholm 

Thanks for response. I am looking at some data with "spikes" and over time, they can be "choppy" as well; not as you said, differentiable for both m and n, which is the main reason, I didn't turn them into ODEs.

For my first encounter with Maple, I have fitted the data with parametric function m(x) and n(y). But I will have to face the reality that the data are not differentiable next.

Note the following change, which is dfferent from your code.

myeq:=f(x)=1-1*int((m(x)/0.6+n(y))*f(y),y=0..x);

@Rouben Rostamian  

thanks for the fix; and tomleslie's comments.

I have made three revisions

1. the equation as:

myeq:=f(x)=1-1*int((s(x)/0.6+r(y))*f(y),y=0..x);

2. To avoid division by zero for y, I revised the y=y+0.00001 for denominator within integration; it worked for me.

3. I am not used to reading Maple's output. I used this line to execute the call of intsolve.

intsolve(myeq,f(x),method=Neumann, order=5);

I find my solution after a long while (40 minutes); part of it pasted here.

Question 1: I wonder how to read them? K1? K1^2?? where can I find more information about reading outputs like this? In order to speed up the solving, which is very slow for 8GB ram Intel i7.

Question 2: Is there a way to plug this back into the u(x) to check if it returns my LHS=RHS?

m:x->-0.028+0.0318*(1-exp(-x/10))/(x/10)+0.0657*((1-exp(-x/10))/(x/10)-exp(-x/10));
n:=y->0.0682-0.02*(1-exp(-y/2.479))/(y/2.479)-0.0606*((1-exp(-y/2.479))/(y/2.479)-exp(-y/2.479));
myeq:=u(x)-1*int((m(x)/0.6+n(y))*u(y),y=0..x);
myeq;
intsolve(myeq,u(x),method=Neumann,order=10);

I wonder if anyone tried running these lines; I have no results no error messages returned. Am I supposed to see error messages if the code is wrong?

@tomleslie Many thanks for the previous two response.

I just installed Maple today. Sorry for the picture instead of texts I posted. I am still trying to find my way around in Maple. I notice I was using 2d-input; thanks for the comments. I will be posting the scripts soon after I retype them.