Differential Equations

[bshoring]

Thanks everyone for your kind explanations and suggestions. I'll check out the book 'Differential Equations with Applications and Historical Notes', by George F. Simmons.

I think I'm a little closer to understanding what's going on.

I have played around with the program by Fernando del Rey at the bottom of Valentin's article "Long Live the HP-25 ! I have plugged into it the formula for calculating Simple Interest on the basis of a 365-day year with the formula:
(n/365)*PV*i = INT (simple interest)
where PV (present value)=5,000 and i=.05 and n is provided by the program and is subject to change.

Using this formula we get:
1 day INT= .684932
2 days " = 1.369863
3 " " = 2.054795
4 " " = 2.739726
5 " " = 3.424658

Now when I run the 4th order Differential Equations program and store initial values of 0 in R1 and R2 and a step size of 1 in R0, I get the following results at steps 1 through 5:
1. .342466 (50% of 1 day's interest)
2. 1.369863 (100% of 2 day's interest)
3. 3.082192 (150% of 3 day's interest)
4. 5.479452 (200% of 4 day's interest)
5. 8.561644 (250% of 5 day's interest)

So I can see that at each step there is some relationship to the actual interest. But what I don't yet get is, "What are these numbers trying to tell me?"

The other question that comes to mind is, what is the difference between a first order vs 3rd order or 4th order Differential Equations? Is it a matter of the higher the order the greater the accuracy or is there some other issue?

Again, thanks all for all your kind explanations and patience!