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Re: Differential equations and notation

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: Differential equations and notation
• From: winkel at nextwork.rose-hulman.edu
• Date: Fri, 16 Oct 92 17:11:58 EST

Hello

I enjoy reading a number of user group activities. One of them is the Maple  
group.  I recently found this message of interest.

>I am trying to know if Maple can solve the following equation:
>   g:=(a*t^2+b)*diff(diff(f(t),t),t)+c*t*diff(f(t),t)+d*f(t)=e;
>
>with values
>	a:=335/10000;
>	c:=154/1000;
>	b:=129/1000;
>	d:=46872/1000;
>	e:=544/10000;

There was some reply indicating Maple would not solve this equation.
I tried the equation on Mathematica and it would not DSolve it either.   It  
quickly (1.05 seconds) NDSolve'd the differential equation with initial  
conditions f(0 = 1 and f'(0) = 1) in the t interval [0, 5] and I used  
Mathematica's resulting InterpolatingFunction solution to plot out a nice  
wavy graph.  I also noted the author of a response to the original problem  
indicated there is a solution in terms of hypergeometric functions which  
readily exist in Mathematica as well.

My point is not the differential equation per se, but notation.  I understand  
the choice of computer algebra systems (e.g. Maple) or systems for doing  
mathematics by computer (Mathematica)  can be akin to religion.   
Moreover, I understand Mathematica has its share of cumbersome  
notation.  But I  could not help but look at the statement of a differential  
equation above in Maple syntax:

(a*t^2+b)*diff(diff(f(t),t),t)+c*t*diff(f(t),t)+d*f(t)=e

and compare it to the corresponding syntax both visually and  
mathematically in Mathematica 


(a t^2 + b) f''[t] + c t f'[t] + d f[t] == e.


Brian J. Winkel, Editor
PRIMUS, Cryptologia, Collegiate Microcomputer
Department of Mathematics
Rose-Hulman Institute of Technology
Terre Haute IN 47803 USA
PHONE: 812-877-8412:  FAX 812-877-3198
email:  winkel at nextwork.rose-hulman.edu