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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
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