Your reply has been really helpful. Thank you very much.
I have the following questions. They are rather trivial ones. I just want to know how far I can go in using Maple to navigate through algebraic manipulations that one normally goes through manually on a written page.
1. From the expressions for I2 and d2 (i.e. the integral and its derivative w.r.t b in my previous post), I would like to know how I can use Maple in arriving at the differential equation, diffeq. I arrived at it by multiplying the integral I2 by the expression ((1+w^2)-w^2). The first term in the resulting integral is the integral, I1 which has a known solution. The second term is -d2/(2*b), where d2 is the derivative of I2. From this, the following differential equation is arrived at :
diffeq:= diff(J(b), b) - 2*J(b)*b = -sqrt(Pi)*exp(-2*a*b);
The question is, can this be done via Maple? How can I lead Maple to this differential equation? Or is this kind of wish not something to be pursued?
2. Following in the same track, I would like to go further with the solution for the differential equation that you presented for me. I would like to substitute the value of 0 for b to evaluate the constant _C1. And, from that, to get the final solution for the integral I2. I know that I can use the subs command and get the value of the expression for J(0). But I want to go beyond that and replicate manual derivations with Maple. As I mentioned before, these are quite trivial pursuits. But if such a skill is acquired, it coud be useful to go through long derivations without making some simple algebraic mistakes.
I truly appreciate the help that I have obtained here. Unfortunately, I find that I don't have the right to vote. If I could, I would have given several votes.